arXiv subjects

Ettore Vicari

Publications and source records attributed to Ettore Vicari.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic scaling behavior in the presence of a periodic magnetic driving across Ising continuous transitions

We study the critical dynamics arising from a time-dependent periodic homogenous source coupled to the order-parameter field, which drives a classical ferromagnetic system across a continuous transition. For this purpose, we consider the paradigmatic two-dimensional (2D) Ising model in the presence of a periodic magnetic field $h(t)=-A\, \cos (2\pi t/P)$, evolving under a purely relaxational dynamics at the critical temperature. We show that the periodic driving gives rise to a peculiar dynamic scaling behavior in the thermodynamic limit, arising from a nontrivial interplay among the time $t$, the amplitude $A$ and period $P$ of $h(t)$. The relevant scaling variables are $\tau=t/P$ and $\sigma=A P^\kappa$, with $\kappa = y_h/z$, where $y_h=(d+2-\eta)/2$ is the critical dimension of the magnetic field, and $z$ is dynamic exponent for the critical relaxational dynamics ($\kappa\approx 0.865$ for the 2D Ising model). The dynamic scaling behaviors of the magnetization and bond-energy density show an oscillatory behavior around a smooth curve which approaches a large-$\tau$ stationary behavior. We also briefly discuss the dynamic behavior of an Ising system driven across the critical point by a periodic time-varying temperature at zero magnetic field.

cond-mat.stat-mech↗

arXiv2026

Charged Abelian Higgs phase transitions in three-dimensional compact lattice U(1) gauge models with multicharge scalar matter

We consider three-dimensional (3D) lattice Abelian Higgs models, with compact U(1) gauge variables coupled to a doubly-charged $N$-component complex scalar field (CLAH). We focus on their phase transitions between the disordered-confined (DC) and ordered-deconfined (OD) phases. When they are continuous they belong to the 3D Abelian Higgs (AH) universality class associated with the stable charged fixed point (CFP) of the renormalization-group flow of the 3D AH field theory, or scalar electrodynamics, describing $N$-component complex scalar fields minimally coupled to a U(1) gauge field. This CFP exists only for a sufficiently large number of components, i.e., $N \ge N_d^*$, where the integer $N_d^*$ depends on the spatial dimension $d$ (for example $N_4^*=183$). To estimate $N_3^*$, we look for the minimum number $N_{\rm cL}$ of scalar components of 3D doubly-charged CLAH models developing continuous transitions along their DC-OD transition line. For this purpose, we present finite-size scaling analyses of Monte Carlo simulations for $N\in[4,10]$, up to lattice sizes $L\approx 100$. The results provide evidence of continuous DC-OD transitions for $N=10$, and weak first-order transitions for $N\le 7$. They are not conclusive for $N=8,\,9$. Therefore, we estimate $N_{\rm cL}=9(1)$.

cond-mat.stat-mech↗

arXiv2026

Spinodal-like scaling behavior after a temperature quench across the first-order phase transition in three-dimensional $q$-state Potts models

We study the out-of-equilibrium spinodal-like behavior of three-dimensional (3D) $q$-state Potts models (for $q\ge 3$), observed when the temperature is quenched across the first-order transition (FOT) point $\beta_{\rm fo}=T_{\rm fo}^{-1}$. We consider a standard quench protocol, in which high-temperature configurations, thermalized at $\beta_i<\beta_{\rm fo}$, are driven across the FOT by a purely relaxational dynamics at $\beta>\beta_{\rm fo}$. We focus on the emergence of spinodal-like behaviors in the thermodynamic limit, associated with the dynamic phase change. We argue that, if the nucleation of smooth droplets is the relevant mechanism of the post-quench phase change, for sufficiently small $\beta_{\rm fo}-\beta_i>0$, the time-dependent energy density should scale in terms of $\rho = (\ln t)^{3/2} \delta$, where $\delta = \beta/\beta_{\rm fo}-1$, with a discontinuity at a particular value $\rho=\rho_s>0$. This implies the emergence of a spinodal-like behavior, whose time scale $\tau$ increases exponentially as $\ln \tau \approx (\rho_s/\delta)^{2/3}$ in the limit $\delta\to 0^+$. We present a numerical analysis of the quench protocol in the 3D $q=6$ Potts model, which supports the above spinodal-like scenario.

cond-mat.stat-mech↗

arXiv2026

Out-of-equilibrium percolation transitions at finite critical times after quenches across magnetic first-order transitions

We show that an out-of-equilibrium percolation transition occurs after quenching ferromagnetic Ising-like systems across their magnetic first-order transitions. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature first-order transition line by a quench of the magnetic field $h$ from $h_i<0$ to $h>0$. In the thermodynamic limit and for finite values of $h$, the post-quench evolution under a purely relaxational dynamics is characterized by a dynamic transition at a finite critical time $t_c(h)$ from the metastable negatively magnetized phase to the positive one, marked by the percolation of the largest clusters of positive and negative spins. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on $h$. We also show that the percolation critical behavior is related to the spinodal-like behavior of the magnetization in the small-$h$ limit, which implies that the percolation time $t_c(h)$ exhibits a spinodal-like exponential dependence on $h$.

cond-mat.stat-mech↗

arXiv2026

Effects of quenched disorder in three-dimensional lattice ${\mathbb Z}_2$ gauge Higgs models

We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice ${\mathbb Z}_2$ gauge Higgs models. For this purpose, we consider two types of quenched disorder, associated with the sites and plaquettes of the cubic lattice. In both cases, for sufficiently weak disorder, the phase diagram remains similar to that of the pure system, showing two different phases (one of them being a topologically ordered phase), separated by two different continuous transition lines. However, the quenched disorder changes the universality classes of the critical behaviors along some of the transition lines. The random-plaquette disorder turns out to be relevant along the topological ${\mathbb Z}_2$ gauge transition line, so the critical behaviors belong to the different random-plaquette $\mathbb{Z}_2$ gauge (RP${\mathbb Z}_2$G) universality class with length-scale exponent $\nu=\nu_{\rm rp}\approx 0.82$; on the other hand, it turns out to be irrelevant along the other Ising$^\times$ transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with $\nu=\nu_{\cal I}\approx 0.63$. The random-site disorder leads to a substantially different scenario: it destabilizes the Ising$^\times$ critical behaviors of the pure model, changing them into those of the randomly-dilute Ising$^{\times}$ (RDI$^{\times}$) universality class with $\nu=\nu_{\rm rdi}\approx 0.68$, while the critical behaviors along the other ${\mathbb Z}_2$ gauge topological transition line remains stable, with $\nu=\nu_{\cal I}\approx 0.63$.

cond-mat.dis-nn↗

arXiv2026

Stacked quantum Ising systems and quantum Ashkin-Teller model

We analyze the quantum states of an isolated composite system consisting of two stacked quantum Ising (SQI) subsystems, coupled by a local Hamiltonian term that preserves the $Z_2$ symmetry of each subsystem. The coupling strength is controlled by an intercoupling parameter $w$, with $w=0$ corresponding to decoupled quantum Ising systems. We focus on the quantum correlations of one of the two SQI subsystems, $S$, in the ground state of the global system, and study their dependence on both the state of the weakly-coupled complementary part $E$ and the intercoupling strength. We concentrate on regimes in which $S$ develops critical long-range correlations. The most interesting physical scenario arises when both SQI subsystems are critical. In particular, for identical SQI subsystems, the global system is equivalent to the quantum Ashkin-Teller model, characterized by an additional $Z_2$ interchange symmetry between the two subsystem operators. In this limit, one-dimensional SQI systems exhibit a peculiar critical line along which the length-scale critical exponent $\nu$ varies continuously with $w$, while two-dimensional systems develop quantum multicritical behaviors characterized by an effective enlargement of the symmetry of the critical modes, from the actual $Z_2\oplus Z_2$ symmetry to a continuous O(2) symmetry.

cond-mat.stat-mech↗

arXiv2026

Finite-temperature topological transitions in the presence of quenched uncorrelated disorder

We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in which the defect dynamics is very slow. As a paradigmatic model, we consider the classical three-dimensional lattice ${\mathbb Z}_2$ gauge model in the presence of quenched uncorrelated disorder associated with the plaquettes of the lattice, whose topological transitions are characterized by the absence of a local order parameter. We study the critical behaviors in the presence of weak disorder. We show that they belong to a new topological universality class, different from that of the lattice ${\mathbb Z}_2$ gauge models without disorder, in agreement with the Harris criterium for the relevance of uncorrelated quenched disorder when the pure system undergoes a continuous transition with positive specific-heat critical exponent.

cond-mat.dis-nn↗

arXiv2025

Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse ($g$) and longitudinal ($h$) magnetic fields. This model exhibits a continuous quantum transition (CQT) at $g=g_c$ and $h=0$, and first-order quantum transitions (FOQTs) driven by $h$ along the line $h=0$ ($g 0$. We focus on values of $h_f$ such that the spectrum of the post-QQ Hamiltonian $H(g,h_f)$ lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of $g$, finding qualitatively distinct behaviors for $g > g_c$ (where the chain is in the disordered phase), for $g = g_c$ (QQ across the CQT), and for $g<g_c$ (QQ across the FOQT line).

cond-mat.stat-mech↗

arXiv2025

Out-of-equilibrium spinodal-like scaling behaviors across the magnetic first-order transitions of 2D and 3D Ising systems

We study the out-of-equilibrium scaling behavior of two-dimensional and three-dimensional Ising systems, when they are slowly driven across their {\em magnetic} first-order transitions at low temperature $T 0$ of the magnetic field, which decrease as $h_* \sim 1/(\ln t_s)^κ$, with $κ= 2$ and $κ=1$ in two and three dimensions, respectively, for $t_s\to\infty$. We identify $σ\equiv t (\ln t)^κ/t_s$ as the relevant scaling variable associated with the KZ dynamics in the TL.

cond-mat.stat-mech↗

arXiv2025

Out-of-equilibrium spinodal-like scaling behaviors at the thermal first-order transitions of three-dimensional q-state Potts models

We study the out-of-equilibrium spinodal-like dynamics of three-dimensional $q$-state Potts systems driven across their thermal first-order transition in the thermodynamic limit, by a relaxational (heat-bath) dynamics. During the evolution, the inverse temperature $\beta$ increases linearly with time, as $\delta\beta(t)\equiv \beta(t)- \beta_{\rm fo} \sim t/t_s$, where $\beta_{\rm fo}$ is the inverse temperature at the transition point, $t$ is the time and $t_s$ is a time scale. The dynamics starts at $t_i< 0$ from an ensemble of disordered configurations equilibrated at inverse temperature $\beta(t_i)<\beta_{\rm fo}$ and ends at positive values of $t$, when the system is ordered (this is analogous to a standard Kibble-Zurek protocol). The time-dependent energy density shows an out-of-equilibrium scaling behavior in the large-$t_s$ limit, in terms of the scaling variable $t(\ln t)^\kappa/t_s$. The corresponding exponent turns out to be consistent with $\kappa=3/2$ (with a good accuracy), which is the value obtained by assuming that the initial nucleation of ordered regions provides the relevant mechanism for the passage from one phase to the other. The scaling behavior implies a spinodal-like phenomenon close to the transition point: the passage from the disordered to the ordered phase, composed of large ordered regions of different color, occurs at $\delta\beta(t)=\delta\beta_*>0$, where $\delta\beta_*$ decreases as $1/(\ln t_s)^{3/2}$ in the large-$t_s$ limit.

cond-mat.stat-mech↗

arXiv2025

Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions

A fundamental issue in the renormalization-group (RG) theory of critical phenomena concerns the allowed values of critical exponents that are consistent with the continuous nature of a phase transition. Here we conjecture a lower bound for the length-scale exponent $\nu$, which should hold for the large class of continuous transitions associated with $d$-dimensional Landau-Ginzburg-Wilson (LGW) $\Phi^4$ theories with a multicomponent scalar field ${\varphi}$ and a unique ${\varphi}\cdot {\varphi}$ quadratic term (including some extensions with fermionic and gauge fields), describing many universality classes of critical phenomena. If $\Delta_\varphi=(d-2+\eta)/2$ is the dimension of the order-parameter field ${\varphi}$, and $\Delta_\varepsilon=d-1/\nu$ is the RG dimension of the energy operator $\varepsilon$, which can be identified with $[{\varphi}\cdot {\varphi}]$ (the squared field with a proper subtraction of the mixing with the identity), we conjecture the inequality $\Delta_\varepsilon \ge 2 \Delta_\varphi$, which implies $\nu \ge (2-\eta)^{-1}$ and $\gamma = (2-\eta)\nu\ge 1$. These inequalities are supported by general arguments for ferromagnetic lattice models, by $\epsilon$-expansion results for generic LGW $\Phi^4$ theories close to four dimensions, exact relations for two-dimensional minimal conformal field theories, and are consistent with all further known (numerical, perturbative, and exact) results for LGW $\Phi^4$ theories. In particular, since unitarity requires $\eta\ge 0$, the above inequality implies $\nu\ge 1/2$ for unitary theories. This lower bound is more restrictive than $\nu > 1/d$, derived by noting that $\nu=1/d$ characterizes the singular finite-size behavior at first-order transitions.

cond-mat.stat-mech↗

arXiv2025

Scaling behaviors at quantum and classical first-order transitions

We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory appropriate to describe the general features of the large-scale, and long-time for dynamic phenomena, behavior of finite-size systems.

cond-mat.stat-mech↗

arXiv2025

Kibble-Zurek dynamics across the first-order quantum transitions of quantum Ising chains in the thermodynamic limit

We study the out-of-equilibrium Kibble-Zurek (KZ) dynamics in quantum Ising chains in a transverse field, driven by a time-dependent longitudinal field $h(t)=t/t_s$ ($t_s$ is the time scale of the protocol), across their first-order quantum transitions (FOQTs) at $h=0$. The KZ protocol starts at time $t_i<0$ from the negatively magnetized ground state for $h_i = t_i/t_s<0$. Then, the system evolves unitarily up to a time $t_f > 0$, such that the magnetization of the state at time $t_f$ is positive. In finite-size systems, the KZ dynamics develops out-of-equilibrium finite-size scaling (OFSS) behaviors. Their scaling variables depend either exponentially or with a power law on the size, depending on the boundary conditions (BC). The OFSS functions can be computed in effective models restricted to appropriate low-energy (magnetized and/or kink) states. The KZ scaling behavior drastically changes in the thermodynamic limit (TL), defined as the infinite-size limit keeping $t$ and $t_s$ fixed, which appears substantially unrelated with the OFSS regime, because it involves higher-energy multi-kink states, which are irrelevant in the OFSS limit. The numerical analyses of the KZ dynamics in the TL show the emergence of a quantum spinodal-like scaling behavior at the FOQTs for all considered BC, which is independent of the BC. The longitudinal magnetization changes sign at $h(t)=h*>0$, where $h*$ decreases with increasing $t_s$, as $h*\sim 1/\ln t_s$. Moreover, in the large-$t_s$ limit, the time-dependence of the magnetization is described by a universal function of $Ω= t/τ_s$, with $τ_s = t_s/\ln t_s$.

cond-mat.stat-mech↗

arXiv2025

Three-dimensional Abelian and non-Abelian gauge Higgs theories

Gauge symmetries and Higgs mechanisms are key features of theories describing high-energy particle physics and collective phenomena in statistical and condensed-matter physics. In this review we address the collective behavior of systems of multicomponent scalar fields interacting with gauge fields, which can be already present in the underlying microscopic system or emerge only at criticality. The interplay between local gauge and global symmetries determines the phase diagram, the nature of the Higgs phases, and the nature of phase transitions between the high-temperature disordered and the low-temperature Higgs phases. However, additional crucial features determine the universal properties of the critical behavior at continuous transitions. Specifically, their nature also depends on the role played by the gauge modes at criticality. Effective (Abelian or non-Abelian) gauge Higgs field theories emerge when gauge modes develop critical correlations. On the other hand, a more standard critical behavior, which admits an effective description in terms of Landau-Ginzburg-Wilson $Φ^4$ theories, occurs when gauge-field modes are short ranged at the transition. In the latter case, gauge fields only prevent non-gauge invariant correlation functions from becoming critical. This review covers the recent progress made in the study of Higgs systems with Abelian and non-Abelian gauge fields. We discuss the equilibrium thermodynamic properties of systems with a classical partition function, focusing mainly on three-dimensional systems, and only briefly discussing two-dimensional models. However, by using the quantum-to-classical mapping, the results on the critical behavior for classical systems in $D=d+1$ dimensions can be extended to quantum transitions in $d$ dimensions.

cond-mat.stat-mech↗

arXiv2025

Critical dynamics of three-dimensional $Z_N$ gauge models and the inverted XY universality class

We investigate the critical relaxational dynamics of the three-dimensional (3D) lattice $Z_N$ gauge models with $N=6$ and $N=8$, whose equilibrium critical behavior at their topological transitions belongs to the inverted XY (IXY) universality class (this is also the universality class of the continuous transitions of the 3D lattice U(1) gauge Higgs models with a one-component complex scalar field), which is connected to the standard XY universality class by a nonlocal duality relation of the partition functions. Specifically, we consider the purely relaxational dynamics realized by a locally reversible Metropolis dynamics, as commonly used in Monte Carlo simulations. To determine the corresponding dynamic exponent $z$, we focus on the out-of-equilibrium critical relaxational flows arising from instantaneous quenches to the critical point, which are analyzed within an out-of-equilibrium finite-size scaling framework. We obtain the estimate $z=2.59(3)$. A numerical analysis of the equilibrium critical dynamics give consistent, but less accurate, results. This dynamic exponent is expected to characterize the critical slowing down of the purely relaxational dynamics of all topological transitions that belong to the 3D IXY universality class. We note that this result implies that the critical relaxational dynamics of the 3D IXY universality class is slower than that of the standard 3D XY universality class, whose relaxational dynamic exponent $z\approx 2.02$ is significantly smaller, although they share the same length-scale critical exponent $ν\approx 0.6717$.

cond-mat.stat-mech↗

arXiv2025

Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models

We study the out-of-equilibrium dynamics of one-dimensional quantum Ising models in a transverse field $g$, driven by a time-dependent longitudinal field $h$ across their {\em magnetic} first-order quantum transition at $h=0$, for sufficiently small values of $|g|$. We consider nearest-neighbor Ising chains of size $L$ with periodic boundary conditions. We focus on the out-of-equilibrium behavior arising from Kibble-Zurek protocols, in which $h$ is varied linearly in time with time scale $t_s$, i.e., $h(t)=t/t_s$. The system starts from the ground state at $h_i\equiv h(t_i)<0$, where the longitudinal magnetization $M$ is negative. Then it evolves unitarily up to positive values of $h(t)$, where $M(t)$ becomes eventually positive. We identify several scaling regimes characterized by a nontrivial interplay between the size $L$ and the time scale $t_s$, which can be observed when the system is close to one of the many avoided level crossings that occur for $h\ge 0$. In the $L\to\infty$ limit, all these crossings approach $h=0^+$, making the study of the thermodynamic limit, defined as the limit $L\to\infty$ keeping $t$ and $t_s$ constant, problematic. We study such limit numerically, by first determining the large-$L$ quantum evolution at fixed $t_s$, and then analyzing its behavior with increasing $t_s$. Our analysis shows that the system switches from the initial state with $M<0$ to a positively magnetized state at $h = h_*(t_s)>0$, where $h_*(t_s)$ decreases with increasing $t_s$, apparently as $h_*\sim 1/\ln t_s$. This suggests the existence of a scaling behavior in terms of the rescaled time $Ω= t \ln t_s/t_s$. The numerical results also show that the system converges to a nontrivial stationary state in the large-$t$ limit, characterized by an energy significantly larger than that of the corresponding homogeneously magnetized ground state.

cond-mat.stat-mech↗

arXiv2025

Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU($N_c$) gauge Higgs models

We consider the three-dimensional (3D) lattice SU($N_c$) gauge Higgs theories with multicomponent ($N_f>1$) degenerate scalar fields and U($N_f$) global symmetry, focusing on systems with $N_c=2$, to identify critical behaviors that can be effectively described by the corresponding 3D SU($N_c$) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of $N_f$, that would control transitions characterized by the global symmetry-breaking pattern ${\rm U}(N_f)\rightarrow \mathrm{SU}(2)\otimes \mathrm{U}(N_f-2)$. Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for $N_f \ge 30$. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of $N_f$. The results are in substantial agreement with the field-theoretical predictions obtained in the large-$N_f$ limit. This provides evidence that the SU($N_c$) gauge Higgs field theories provide the correct effective description of the 3D large-$N_f$ continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to $\mathrm{SU}(2)\otimes \mathrm{U}(N_f-2)$. Therefore, at least for large enough $N_f$, the 3D SU($N_c$) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretizatized models with the same local and global symmetries.

hep-lat↗

arXiv2025

Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb Z}_2$ gauge symmetry

We characterize the dynamic universality classes of a relaxational dynamics under equilibrium conditions at the continuous transitions of three-dimensional (3D) spin systems with a ${\mathbb Z}_2$-gauge symmetry. In particular, we consider the pure lattice ${\mathbb Z}_2$-gauge model and the lattice ${\mathbb Z}_2$-gauge XY model, which present various types of transitions: topological transitions without a local order parameter and transitions characterized by both gauge-invariant and non-gauge-invariant XY order parameters. We consider a standard relaxational (locally reversible) Metropolis dynamics and determine the dynamic critical exponent $z$ that characterizes the critical slowing down of the dynamics as the continuous transition is approached. At the topological ${\mathbb Z}_2$-gauge transitions we find $z=2.55(6)$. Therefore, the dynamics is significantly slower than in Ising systems -- $z\approx 2.02$ for the 3D Ising universality class -- although 3D ${\mathbb Z}_2$-gauge systems and Ising systems have the same static critical behavior because of duality. As for the nontopological transitions in the 3D ${\mathbb Z}_2$-gauge XY model, we find that their critical dynamics belong to the same dynamic universality class as the relaxational dynamics in ungauged XY systems, independently of the gauge-invariant or nongauge-invariant nature of the order parameter at the transition.

cond-mat.stat-mech↗