arXiv subjects

Andrea Pelissetto

Publications and source records attributed to Andrea Pelissetto.

At least 37 records · Page 2Linked to original sources

arXiv2024

Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields

We investigate the nature of the deconfinement transitions in three-dimensional lattice Abelian Higgs models, in which a complex scalar field of integer charge $Q\ge 2$ is minimally coupled with a compact $U(1)$ gauge field. Their phase diagram presents two phases separated by a transition line where static charges $q$, with $q<Q$, deconfine. We argue that these deconfinement transitions belong to the same universality class as transitions in generic three-dimensional ${\mathbb Z}_Q$ gauge models. In particular, they are Ising-like for $Q=2$, of first order for $Q=3$, and belong to the three-dimensional gauge $XY$ universality class for $Q\ge 4$. This general scenario is supported by numerical finite-size scaling analyses of the energy cumulants for $Q=2$, $Q=4$, and $Q=6$.

hep-lat↗

arXiv2024

Diverse universality classes of the topological deconfinement transitions of three-dimensional noncompact lattice Abelian-Higgs models

We study the topological phase transitions occurring in three-dimensional (3D) multicomponent lattice Abelian-Higgs (LAH) models, in which an $N$-component scalar field is minimally coupled with a noncompact Abelian gauge field, with a global SU($N$) symmetry. Their phase diagram presents a high-temperature Coulomb (C) phase, and two low-temperature molecular (M) and Higgs (H) phases, both characterized by the spontaneous breaking of the SU($N$) symmetry. The molecular-Higgs (MH) and Coulomb-Higgs (CH) transitions are topological transitions, separating a phase with gapless gauge modes and confined charges from a phase with gapped gauge modes and deconfined charged excitations. These transitions are not described by effective Landau-Ginzburg-Wilson theories, due to the active role of the gauge modes. We show that the MH and CH transitions belong to different charged universality classes. The CH transitions are associated with the $N$-dependent charged fixed point of the renormalization-group (RG) flow of the 3D Abelian-Higgs field theory (AHFT). On the other hand, the universality class of the MH transitions is independent of $N$ and coincides with that controlling the continuous transitions of the one-component ($N=1$) LAH model. In particular, we verify that the gauge critical behavior always corresponds to that observed in the 3D inverted XY model, and that the correlations of an extended charged gauge-invariant operator (in the Lorenz gauge, this operator corresponds to the scalar field, thus it is local, justifing the use of the RG framework) have an $N$-independent critical universal behavior. This scenario is supported by numerical results for $N=1,\,2,\,25$. The MH critical behavior does not apparently have an interpretation in terms of the RG flow of the AHFT, as determined perturbatively close to four dimensions or with standard large-$N$ methods.

cond-mat.stat-mech↗

arXiv2024

Comment on "Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model'', arXiv:2311.17994v1

We critically discuss the results reported in arXiv:2311.17994v1 by L. Oppenheim, M. Koch-Janusz, S. Gazit, and Z. Ringel, on the multicritical behavior of the three-dimensional Ising-Gauge model at the multicritical point. We argue that their results do not contradict the theoretical scenario put forward in ``Multicritical point of the three-dimensional ${\mathbb Z}_2$ gauge Higgs model'', Phys. Rev. B 105, 165138 (2022), arXiv:2112.01824, that predicted a multicritical behavior controlled by the stable $XY$ fixed point of an effective three-dimensional ${\mathbb Z}_2\oplus {\mathbb Z}_2$ Landau-Ginzburg-Wilson $Φ^4$ field theory. Actually, their results, as well as all numerical results reported so far in the literature, are consistent with a multicritical $XY$ scenario.

cond-mat.stat-mech↗

arXiv2023

Abelian Higgs gauge theories with multicomponent scalar fields and multiparameter scalar potentials

We consider multicomponent Abelian Higgs (AH) gauge theories with multiparameter scalar quartic potentials that are extensions, with a smaller global symmetry group, of $SU(N)$-invariant AH theories. In particular, we consider an AH model with a two-parameter scalar potential and $SO(N)$ global symmetry. We discuss the renormalization-group flow of the $SO(N)$-invariant AH field theory and the phase diagram and critical behavior of a corresponding three-dimensional (3D) noncompact lattice AH model. We argue that the phase diagram of 3D noncompact $SO(N)$- and $SU(N)$-symmetric lattice AH models are qualitatively similar. In both cases there are three phases: the high-temperature Coulomb phase, and the low-temperature molecular and Higgs phases that differ for the topological properties of the gauge correlations. However, the main features of the low-temperature ordered phases, and in particular of the Higgs phase, differ significantly in $SO(N)$ and $SU(N)$ models. In particular, in $SO(N)$ models they depend on the sign of the self-interaction parameter $v$ that controls the symmetry breaking from $SU(N)$ to $SO(N)$. As a consequence, also the universal features of the transitions related with the spontaneous breaking of the global symmetry (those between the high-temperature Coulomb phase and the low-temperature molecular and Higgs phases) depend on the sign of $v$.

cond-mat.stat-mech↗

arXiv2023

Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.

hep-lat↗

arXiv2023

The Coulomb-Higgs phase transition of three-dimensional lattice Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing

We study the critical behavior of three-dimensional (3D) lattice Abelian-Higgs (AH) gauge models with noncompact gauge variables and multicomponent complex scalar fields, along the transition line between the Coulomb and Higgs phases. Previous works that focused on gauge-invariant correlations provided evidence that, for a sufficiently large number of scalar components, these transitions are continuous and associated with the stable charged fixed point of the renormalization-group flow of the 3D AH field theory (scalar electrodynamics), in which charged scalar matter is minimally coupled with an electromagnetic field. Here we extend these studies by considering gauge-dependent correlations of the gauge and matter fields, in the presence of two different gauge fixings, the Lorenz and the axial gauge fixing. Our results for N=25 are definitely consistent with the predictions of the AH field theory and therefore provide additional evidence for the characterization of the 3D AH transitions along the Coulomb-Higgs line as charged transitions in the AH field-theory universality class. Moreover, our results give additional insights on the role of the gauge fixing at charged transitions. In particular, we show that scalar correlations are critical only if a hard Lorenz gauge fixing is imposed.

cond-mat.stat-mech↗

arXiv2023

Gauge fixing and gauge correlations in noncompact Abelian gauge models

We investigate some general properties of linear gauge fixings and gauge-field correlators in lattice models with noncompact U(1) gauge symmetry. In particular, we show that, even in the presence of a gauge fixing, some gauge-field observables (like the photon-mass operator) are not well-defined, depending on the specific gauge fixing adopted and on its implementation. Numerical tests carried out in the three-dimensional noncompact lattice Abelian Higgs model fully support the analytical results and provide further insights.

hep-lat↗

arXiv2022

Chiral critical behavior of 3D lattice fermionic models with quartic interactions

We study the critical behavior of the three-dimensional (3D) Gross-Neveu (GN) model with $N_f$ Dirac fermionic flavors and quartic interactions, at the chiral ${\mathbb Z}_2$ transition in the massless ${\mathbb Z}_2$-symmetric limit. For this purpose, we consider a lattice GN model with staggered Kogut-Susskind fermions and a scalar field coupled to the scalar bilinear fermionic operator, which effectively realizes the attractive four-fermion interaction. We perform Monte Carlo (MC) simulations for $N_f=4,8,12,16$. By means of finite-size scaling analyses of the numerical data, we obtain estimates of the critical exponents that are compared with the large-$N_f$ predictions obtained using the continuum GN field theory. We observe a substantial agreement. This confirms that lattice GN models with staggered fermions provide a nonpertubative realization of the GN quantum field theory, even though the lattice interactions explicitly break the flavor ${\rm U}(N_f)\otimes {\rm U}(N_f)$ symmetry of the GN field theory, which is only recovered in the critical limit.

hep-lat↗

arXiv2022

Multicomponent gauge-Higgs models with discrete Abelian gauge groups

We consider a variant of the charge-Q compact Abelian-Higgs model, in which an Nf-dimensional complex vector is coupled with an Abelian Z_q gauge field. For Nf=2 and Q=1 we observe several transition lines that belong to the O(4), O(3), and O(2) vector universality classes, depending on the symmetry breaking pattern at the transition. The universality class is independent of $q$ as long as q>=3. The universality class of the transition is uniquely determined by the behavior of the scalar fields; gauge fields do not play any role. We also investigate the system for Nf=15 and Q=2. In the presence of U(1) gauge fields, the system undergoes transitions associated with charged fixed points of the Abelian-Higgs field theory. These continuous transitions turn into first-order ones when the U(1) gauge fields are replaced by the discrete Z_q fields: in the present compact model charged transitions appear to be very sensitive to the nature of the gauge fields

hep-lat↗

arXiv2022

Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system

We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a soft quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.

cond-mat.stat-mech↗

arXiv2022

Scalar gauge-Higgs models with discrete Abelian symmetry groups

We investigate the phase diagram and the nature of the phase transitions of three-dimensional lattice gauge-Higgs models obtained by gauging the Z_N subgroup of the global Z_q invariance group of the Z_q clock model (N is a submultiple of q). The phase diagram is generally characterized by the presence of three different phases, separated by three distinct transition lines. We investigate the critical behavior along the two transition lines characterized by the ordering of the scalar field. Along the transition line separating the disordered-confined phase from the ordered-deconfined phase, standard arguments within the Landau-Ginzburg-Wilson framework predict that the behavior is the same as in a generic ferromagnetic model with Z_p global symmetry, p being the ratio q/N. Thus, continuous transitions belong to the Ising and to the O(2) universality class for p=2 and p>3, respectively, while for p=3 only first-order transitions are possible. The results of Monte Carlo simulations confirm these predictions. There is also a second transition line, which separates two phases in which gauge fields are essentially ordered. Along this line we observe the same critical behavior as in the Z_q clock model, as it occurs in the absence of gauge fields.

cond-mat.stat-mech↗

arXiv2022

Three-dimensional monopole-free CP$^{N-1}$ models: Behavior in the presence of a quartic potential

We investigate the phase diagram and the nature of the phase transitions in a three-dimensional model characterized by a global SU($N$) symmetry, a local U(1) symmetry, and the absence of monopoles. It represents a natural generalization of the gauge monopole-free (MF) CP$^{N-1}$ model, in which the fixed-length constraint (London limit) is relaxed. We have performed Monte Carlo simulations for $N=2$ and 25, observing a finite-temperature transition in both cases, related to the condensation of a local gauge-invariant order parameter. For $N=2$ results for the MF model are consistent with a weak first-order transition. A continuous transition would be possible only if scaling corrections were anomalously large. For $N=25$ the results in the general MF model are also consistent with a first-order transition, that becomes weaker as the size of the field-length fluctuations decreases.

cond-mat.stat-mech↗

arXiv2022

Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials

We consider three-dimensional lattice SU(Nc) gauge theories with degenerate multicomponent (Nf>1) complex scalar fields that transform under the fundamental representation of the gauge SU(Nc) group and of the global U(Nf) invariance group, interacting with the most general quartic potential compatible with the global (flavor) and gauge (color) symmetries. We investigate the phase diagrams, identifying the low-temperature Higgs phases and their global and gauge symmetries, and the critical behaviors along the different transition lines. In particular, we address the role of the quartic scalar potential, which determines the Higgs phases and the corresponding symmetry-breaking patterns. Our study is based on the analysis of the minimum-energy configurations and on numerical Monte Carlo simulations. Moreover, we investigate whether some of the transitions observed in the lattice model can be related to the behavior of the renormalization-group flow of the continuum field theory with the same symmetries and field content around its stable charged fixed points. For Nc=2, numerical results are consistent with the existence of charged critical behaviors for Nf > Nf*, with 20 < Nf* < 40.

cond-mat.stat-mech↗

arXiv2022

Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory

We investigate under which conditions the three-dimensional (3D) multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the continuum limit of statistical lattice gauge models, i.e., when it characterizes the universal behavior at critical transitions occurring in these models. We perform Monte Carlo simulations of the lattice AH model with compact gauge fields and $N$-component scalar fields with charge $q\ge 2$ for $N=15$ and 25. Finite-size scaling analyses of the Monte Carlo data show that the transitions along the line separating the confined and deconfined phases are continuous and that they belong to the same universality class for any $q\ge 2$. Moreover, they are in the same universality class as the transitions in the lattice AH model with noncompact gauge fields along the Coulomb-to-Higgs transition line. We finally argue that these critical behaviors are described by the stable charged fixed point of the renormalization-group flow of the 3D AH field theory.

cond-mat.stat-mech↗

arXiv2021

Multicritical point of the three-dimensional Z_2 gauge Higgs model

We investigate the multicritical behavior of the three-dimensional Z_2 gauge Higgs model, at the multicritical point (MCP) of its phase diagram, where one first-order transition line and two continuous Ising-like transition lines meet. The duality properties of the model determine some features of the multicritical behavior at the MCP located along the self-dual line. Moreover, we argue that the system develops a multicritical XY behavior at the MCP, which is controlled by the stable XY fixed point of the three-dimensional multicritical Landau-Ginzburg-Wilson field theory with two competing scalar fields associated with the continuous Z_2 transition lines meeting at the MCP. This implies an effective enlargement of the symmetry of the multicritical modes at the MCP, to the continuous group O(2). We also provide some numerical results to support the multicritical XY scenario.

cond-mat.stat-mech↗

arXiv2021

Continuum limit of two-dimensional multiflavor scalar gauge theories

We address the interplay between local and global symmetries by analyzing the continuum limit of two-dimensional multicomponent scalar lattice gauge theories, endowed by non-Abelian local and global invariance. These theories are asymptotically free. By exploiting Monte Carlo simulations and finite-size scaling techniques, we provide numerical results concerning the universal behavior of such models in the critical regime. Our results support the conjecture that two-dimensional multiflavor scalar models have the same continuum limit as the $σ$-models associated with symmetric spaces that have the same global symmetry.

hep-lat↗

arXiv2021

Breaking the gauge symmetry in lattice gauge-invariant models

We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a U(1) gauge field. We discuss under which conditions a gauge-symmetry breaking term destabilizes the critical behavior (continuum limit) of the gauge-invariant theory. We find that the gauge symmetry is robust at transitions at which gauge fields are not critical. At charged transitions, where gauge fields are critical, gauge symmetry is lost as soon as the perturbation is added.

hep-lat↗

arXiv2021

Global symmetry breaking in gauge theories: the case of multiflavor scalar chromodynamics

Universal features of continuous phase transitions can be investigated by studying the $ϕ^4$ field theory with the corresponding global symmetry breaking pattern. When gauge symmetries are present, the same technique is usually applied to a gauge-invariant order parameter field, as in the Pisarski-Wilczek analysis of the QCD chiral phase transition. Gauge fields are thus assumed to be irrelevant in the effective critical model, a fact that is however far from trivial. We will investigate the validity of this approach using three-dimensional scalar lattice models with non-abelian global and local symmetries, for which critical exponents and scaling functions can be numerically determined with high accuracy.

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