arXiv subjects

Marco Picco

Publications and source records attributed to Marco Picco.

At least 19 recordsLinked to original sources

arXiv2026

Phase Diagram and Critical Behaviour of the Two-Dimensional Potts Model with Long-Range Quenched Disorder

We study the phase diagram and critical properties of the $q = 3$ and $q = 8$ Potts models with spatially correlated disorder governed by a power-law decay with exponent $a$. Building on the phase diagram proposed by Chippari et al. [3], where a transition from finite-disorder to infinite-disorder fixed points was identified as a function of a, we refine this picture by using wrapping probabilities of Fortuin-Kasteleyn clusters. Furthermore, using magnetic observables, we clarify the physical origin of the double-peak structure in the magnetic susceptibility and establish the validity of the hyper-scaling relation across all investigated regimes.

cond-mat.stat-mech↗

arXiv2026

Critical quench dynamics of Wegner's $\mathbb{Z}_2$ gauge model: a geometric perspective

Wegner's $\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-size scaling analysis, we find that the critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent $z_{\rm p} \simeq 2.6$, consistent with that associated with the energy density, $z_{\rm c}$. Importantly, the value of $z_{\rm p}$ is robust with respect to the initial quench condition and the choice of geometrical objects. Furthermore, we provide a detailed characterization of the kinetics of different geometrical objects during the evolution from the percolation phase. Notably, we observe that the quench dynamics obeys dynamic scaling in terms of a growing lengthscale, $\xi_{\rm p}(t) \sim t^{1/z_{\rm p}}$, despite the absence of a local order parameter.

cond-mat.stat-mech↗

arXiv2026

Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model

We investigate the first two moments of the critical internal energy $E$ in a weakly disordered two-dimensional Baxter eight-vertex model as a function of the system size $L$, evaluated at the pseudo-critical point. Disorder is introduced via an equivalent representation of the pure eight-vertex model in terms of two ferromagnetic Ising models coupled by a four-spin interaction of strength $g_0$, where the Ising couplings consist of a uniform ferromagnetic part $J>0$ supplemented by weak Gaussian spatial disorder. In the critical regime, the model is formulated in terms of interacting Grassmann-Majorana spinor fields with quartic interactions and analyzed, for small positive $g_0$, using a combination of replica and renormalization-group methods. We also run extensive numerical simulations measuring the critical internal energy. Our results show that its relative variance increases with $L$ and approaches a finite constant as $L \to \infty$ for both $\pm g_0$. Hence, fluctuations remain relevant independently of the sign of $g_0$ (and thus of the specific-heat exponent), implying a lack of self-averaging of both the critical internal energy and the free energy. Consequently, reliable estimates of these quantities require averaging over many disorder realizations. In addition, we numerically confirm earlier predictions concerning the absence of self-averaging of the critical internal energy in the disordered Ising model.

cond-mat.stat-mech↗

arXiv2024

The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model

After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a percolation analysis of Wegner's three-dimensional $\mathbb{Z}_2$ lattice gauge model using intensive Monte Carlo simulations and finite-size scaling, offering fresh insights into the topological phase transitions of gauge-invariant systems. We demonstrate that, regardless of the connection rules, geometrical loops, constructed by piercing excited plaquettes percolate precisely at the thermal critical point $T_{\rm c}$, with critical exponents coinciding with those of the loop representation of the dual 3D Ising model. Further, we construct Fortuin-Kasteleyn (FK) clusters in a random-cluster representation, showing that they also percolate at $T_{\rm c}$, enabling access to all thermal critical exponents. Strikingly, the Binder cumulants of the percolation order parameters for both loops and FK clusters reveal a pseudo-first-order transition. This work sheds new light on the critical behavior of pure LGTs, with potential implications for condensed matter systems and quantum error correction.

cond-mat.stat-mech↗

arXiv2024

Magnetic exponent for the long-range bond disordered Potts model

We consider the critical behavior of two-dimensional Potts models in presence of a bond disorder in which the correlation decays as a power law. In some recent work the thermal sector of this theory was investigated by a renormalization group computation based on perturbed conformal field theory. Here we apply the same approach to study instead the magnetic sector. In particular we compute the leading corrections to the Potts spin scaling dimension. Our results include as a special case the long-range disorder Ising model. We compare our prediction to Monte-Carlo simulations. Finally, by studying the magnetization scaling function, we show a clear numerical evidence of a cross-over between the long-range and the short-range class of universality.

cond-mat.dis-nn↗

arXiv2024

Interfaces of the two-dimensional voter model in the context of SLE

This paper investigates various geometrical properties of interfaces of the two-dimensional voter model. Despite its simplicity, the model exhibits dual characteristics, resembling both a critical system with long-range correlations, while also showing a tendency towards order similar to the Ising-Glauber model at zero temperature. This duality is reflected in the geometrical properties of its interfaces, which are examined here from the perspective of Schramm-Loewner evolution. Recent studies have delved into the geometrical properties of these interfaces within different lattice geometries and boundary conditions. We revisit these findings, focusing on a system within a box of linear size $L$ with Dobrushin boundary conditions, where values of the spins are fixed to either $+1$ or $-1$ on two distinct halves of the boundary, in order to enforce the presence of a pinned interface with fixed endpoints (or chordal interface). We also expand the study to compare the geometrical properties of the interfaces of the voter model with those of the critical Ising model and other related models. Scaling arguments and numerical studies suggest that, while locally the chordal interface of the voter model has fractal dimension $d_{\rm f}=3/2$, corresponding to a parameter $\kappa=4$, it becomes straight at large scales, confirming a conjecture made by Holmes et al \cite{holmes}, and ruling out the possibility of describing the chordal interface of the voter model by SLE$_{\kappa}$, for any non zero value of $\kappa$. This contrasts with the critical Ising model, which is described by SLE$_3$, and whose interface fluctuations remain of order $L$, and more generally with related critical models, which are in the same universality class.

cond-mat.stat-mech↗

arXiv2024

Dynamical critical behavior on the Nishimori point of frustrated Ising models

By considering the quench dynamics of two-dimensional frustrated Ising models through numerical simulations, we investigate the dynamical critical behavior on the multicritical Nishimori point (NP). We calculate several dynamical critical exponents, namely, the relaxation exponent $z_{\rm c}$, the autocorrelation exponent $\lambda_{\rm c}$, and the persistence exponent $\theta_{\rm c}$, after a quench from the high temperature phase to the NP. We confirm their universality with respect to the lattice geometry and bond distribution. For a quench from a power-law correlated initial state to the NP, the aging dynamics are much slower. We also look up the issue of multifractality during the critical dynamics by investigating different moments of the spatial correlation function. We observe a single growth law for all the length scales extracted from different moments, indicating that the equilibrium multifractality at the NP does not affect the dynamics.

cond-mat.stat-mech↗

arXiv2023

Finite-size scaling of the random-field Ising model above the upper critical dimension

Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension $D = 7$, i.e., above its upper critical dimension $D_{\rm u} = 6$, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions $D > D_{\rm u}$, linear length scale $L$ should be replaced in finite-size scaling expressions by the effective scale $L_{\rm eff} = L^{D / D_{\rm u}}$. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.

cond-mat.stat-mech↗

arXiv2023

Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach

In this paper we provide new analytic results on two-dimensional $q$-Potts models ($q \geq 2$) in the presence of bond disorder correlations which decay algebraically with distance with exponent $a$. In particular, our results are valid for the long-range bond disordered Ising model ($q=2$). We implement a renormalization group perturbative approach based on conformal perturbation theory. We extend to the long-range case the RG scheme used in [V. Dotsenko, Nucl. Phys. B 455 701 23] for the short-range disorder. Our approach is based on a $2$-loop order double expansion in the positive parameters $(2-a)$ and $(q-2)$. We will show that the Weinrib-Halperin conjecture for the long-range thermal exponent can be violated for a non-Gaussian disorder. We compute the central charges of the long-range fixed points finding a very good agreement with numerical measurements.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model

The $\pm J$ Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value $-J$ with probability $p$ and $+J$ with probability $1-p$. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-dimensional $\pm J$ Ising model, after a quench from different initial conditions to a critical point $T_c(p)$ on the paramagnetic-ferromagnetic (PF) transition line, especially, above, below and at the multicritical Nishimori point (NP). The dynamical critical exponent $z_c$ seems to exhibit non-universal behavior for quenches above and below the NP, which is identified as a pre-asymptotic feature due to the repulsive fixed point at the NP. Whereas, for a quench directly to the NP, the dynamics reaches the asymptotic regime with $z_c \simeq 6.02(6)$. We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution (SLE) with corresponding parameter $\kappa$. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.

cond-mat.stat-mech↗

arXiv2023

Long-range quenched bond disorder in the bi-dimensional Potts model

We study the bi-dimensional $q$-Potts model with long-range bond correlated disorder. Similarly to [C. Chatelain, Phys. Rev. E 89, 032105], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for $q=1,2,3$-Potts models for different values of the power-law decaying exponent $a$. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for $q=1$ and $q=2$, we can conjecture the phase diagram for $q\in [1,4]$. In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of $q$ and $a$. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawning the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.

cond-mat.stat-mech↗

arXiv2022

Freezing vs. equilibration dynamics in the Potts model

We study the quench dynamics of the $q$ Potts model on different bi/tri-dimensional lattice topologies. In particular we are interested in instantaneous quenches from $T_i \rightarrow \infty$ to $T \leq T_s$, where $T_s$ is the (pseudo)-spinodal temperature. The goal is to explain why, in the large-$q$ limit, the low-temperature dynamics freezes on some lattices while, on others, the equilibrium configuration is easily reached. The cubic ($3d$) and the triangular ($2d$) lattices are analysed in detail. We show that the dynamics blocks when lattices have acyclic \textit{unitary structures} while the system goes to the equilibrium when these are cyclic, no matter the coordination number ($z$) of the particular considered lattice.

cond-mat.stat-mech↗

arXiv2021

On the CFT describing the spin clusters in 2d Potts model

We have considered clusters of like spin in the Q-Potts model, the spin Potts clusters. Using Monte Carlo simulations, we studied these clusters on a square lattice with periodic boundary conditions for values of Q in [1,4]. We continue the work initiated with Delfino and Viti (2013) by measuring the universal finite size corrections of the two-point connectivity. The numerical data are perfectly compatible with the CFT prediction, thus supporting the existence of a consistent CFT, still unknown, describing the connectivity Potts spin clusters. We provided in particular new insights on the energy field of such theory. For Q=2, we found a good agreement with the prediction that the Ising spin clusters behave as the Fortuin-Kasteleyn ones at the tri-critical point of the dilute 1-Potts model. We show that the structure constants are likely to be given by the imaginary Liouville structure constants, consistently with the results of Delfino et al. (2013) and of Ang and Sun (2021). For Q different from 2 instead, the structure constants we measure do not correspond to any known bootstrap solutions. The validity of our analysis is backed up by the measures of the spin Potts clusters wrapping probability for Q=3. We evaluate the main critical exponents and the correction to the scaling. A new exact and compact expression for the torus one-point of the Q-Potts energy field is also given.

cond-mat.stat-mech↗

arXiv2021

Metastability in the Potts model: exact results in the large q limit

We study the metastable equilibrium properties of the Potts model with heat-bath transition rates using a novel expansion. The method is especially powerful for large number of state spin variables and it is notably accurate in a rather wide range of temperatures around the phase transition.

cond-mat.stat-mech↗

arXiv2021

Low-temperature universal dynamics of the bidimensional Potts model in the large q limit

We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of large number of states, q >> 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account dynamic scaling is universal.

cond-mat.stat-mech↗

arXiv2021

How many phases nucleate in the bidimensional Potts model?

We study the kinetics of the two-dimensional q > 4-state Potts model after a shallow quench slightly below the critical temperature and above the pseudo spinodal. We use numerical methods and we focus on intermediate values of q, 4 < q < 100. We show that, initially, the system evolves as if it were quenched to the critical temperature. The further decay from the metastable state occurs by nucleation of k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size. This unusual finite size dependence is a consequence of a scaling symmetry underlying the nucleation phenomenon for these parameters.

cond-mat.stat-mech↗

arXiv2020

Spin interfaces and crossing probabilities of spin clusters in parafermionic models

We consider fractal curves in two-dimensional $Z_N$ spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main motivation here is to investigate the correspondence between Schramm-Loewner evolutions (SLE) and conformal field theories with extended conformal algebras (ECFT). By using Monte-Carlo simulation, we compute the fractal dimension of different spin interfaces for the N=3 and N=4 spin models that correspond respectively to the 3 states Potts model and to the Ashkin-Teller model at the Fateev-Zamolodchikov point. These numerical measures, that improve and complete the ones presented in the previous works, are shown to be consistent with SLE/ECFT predictions. We consider then the crossing probability of spin clusters in a rectangular domain. Using a multiple SLE approach, we provide crossing probability formulas for ZN parafarmionic theories. The parafermionic conformal blocks that enter the crossing probability formula are computed by solving a Knhiznik-Zamolodchikov system of rank 3. In the 3 states Potts model case, where the parafermionic blocks coincide with the Virasoro ones, we rederive the crossing formula found by S.M.Flores et al., that is in good agreement with our measures. For N>=4 where the crossing probability satisfies a third order differential equation instead of a second order one, our formulas are new. The theoretical predictions are compared to Monte-Carlo measures taken at N=4 and a fair agreement is found.

hep-th↗

arXiv2020

Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of $Q-$ Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.

hep-th↗