arXiv subjects

Claudio Bonati

Publications and source records attributed to Claudio Bonati.

At least 19 recordsLinked to original sources

arXiv2026

A different kind of continuum limit for the three-dimensional U(1) gauge theory

In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter $\mu$. By tuning $\beta$ and $\mu$ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing $\beta$, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.

hep-lat↗

arXiv2026

Confining Flux Tube in the Trace Deformed (2+1) Dimensional SU(2) Gauge Theory

We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Goto effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.

hep-lat↗

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

Topological Susceptibility and QCD at Finite Theta Angle

In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $\theta$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($\eta^\prime$ physics, neutron electric dipole moment) and beyond (strong CP problem and the axion solution). We then provide an overview of the main analytic predictions for $\theta$-dependence obtained using several different approaches (chiral effective theories, large-$N$ arguments, semiclassical methods) and their regimes of validity, as well as a selection of the most recent numerical results about QCD topology obtained via Monte Carlo simulations of the lattice-discretized theory.

hep-lat↗

arXiv2026

The COSMIC WISPers White Paper: The physics case for Weakly Interacting Slim Particles

Axions and other very weakly interacting slim particles (WISPs), with masses below 1 GeV, arise naturally in many extensions of the Standard Model of particle physics. In particular, they could offer a new framework to explain the nature of dark matter and may help address a range of puzzling observations in astrophysics and particle physics. This review provides an overview of ongoing WISP searches and outlines the prospects for the next decade, spanning their theoretical motivation, indirect signatures in astrophysical observations, and dedicated laboratory experiments. It is based on the work carried on by the EU-funded COST Action ``Cosmic WISPers in the Dark Universe: Theory, astrophysics, and experiments'' (CA21106, https://www.cost.eu/actions/CA21106). This network plays a key role in coordinating and supporting WISP searches across Europe, while also contributing to the development of a roadmap aimed at securing European leadership in this research area. It is emphasized that Europe is currently pursuing a rich, diverse, and cost-effective experimental program, with the potential to deliver one or more transformative discoveries.

hep-ph↗

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

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

Strong CP problem, theta term and QCD topological properties

In this chapter we introduce the $\theta$-dependence and the topological properties of QCD, features of the strongly interacting sector which give rise to the strong CP problem in the more general context of the Standard Model of particle physics. We discuss the analytical approaches that can be used to obtain qualitative, or in some cases quantitative, information on the $\theta$-dependence of QCD and QCD-like models, discussing their range of validity and comparing their predictions with the numerical results obtained by means of lattice simulations.

hep-lat↗

arXiv2025

Stability of universal properties against perturbations of the Markov Chain Monte Carlo algorithm

We numerically investigate the stability of universal properties at continuous phase transitions against perturbations of the Markov Chain Monte Carlo algorithm used to simulate the system. We consider the three dimensional XY model as test bed, and both local (single site Metropolis) and global (single cluster) updates, introducing deterministic truncation-like perturbations and stochastic perturbations in the acceptance probabilities. In (almost) all the cases we find a remarkable stability of the universal properties, even against large perturbations of the Markov Chain Monte Carlo algorithm, with critical exponents and scaling curves consistent with those of the standard XY model within statistical uncertainties. Only for the single cluster update with very large truncation error does something different happen, but large scaling corrections prevent us from precisely assessing the critical properties of the transition, and, in particular, to understand whether the critical behavior observed corresponds to a known universality class.

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 $\nu\approx 0.6717$.

cond-mat.stat-mech↗

arXiv2025

O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model

We numerically investigate the multicritical behavior of the three dimensional lattice system in which a SU(2) gauge field is coupled to two flavors of scalar fields transforming in the fundamental representation of the gauge group. In this system a multicritical point is present, where the global symmetry O(2)$\oplus$O(3) gets enlarged to O(5). Such a symmetry enlargement is hindered for generic systems by the instability of the O(5) multicritical point, but the SU(2) gauge symmetry prevents the appearance of the term triggering the instability. All the numerical results obtained in this lattice gauge model fully support the expectations coming from the O(2)$\oplus$O(3) multicritical Landau-Ginzburg-Wilson $\phi^4$ theory, and we discuss possible implications of these results for some models of deconfined quantum criticality.

hep-lat↗

arXiv2025

Out-of-equilibrium critical dynamics of the three-dimensional ${\mathbb Z}_2$ gauge model along critical relaxational flows

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice ${\mathbb Z}_2$ gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link ${\mathbb Z}_2$ gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice ${\mathbb Z}_2$ gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent $z$ associated with the purely relaxational dynamics of the three-dimensional ${\mathbb Z}_2$ gauge universality class. We obtain $z=2.610(15)$, which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.

cond-mat.stat-mech↗

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↗

arXiv2024

The imaginary-$\theta$ dependence of the SU($N$) spectrum

In this talk we will report on a study of the $\theta$-dependence of the string tension and of the mass gap of four-dimensional SU($N$) Yang--Mills theories. The spectrum at $N=3$ and $N=6$ was obtained on the lattice at various imaginary values of the $\theta$-parameter, using Parallel Tempering on Boundary Conditions to avoid topological freezing at fine lattice spacings. The coefficient of the $\mathcal{O}(\theta^2)$ term in the Taylor expansion of the spectrum around $\theta=0$ could be obtained in the continuum limit for $N=3$, and on two fairly fine lattices for $N=6$.

hep-lat↗

arXiv2024

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 $\Phi^4$ 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↗

arXiv2024

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↗

arXiv2024

Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)$^$ and Ising$^$ continuous transitions

We study the O($N$)$^*$ transitions that occur in the 3D $\mathbb{Z}_2$-gauge $N$-vector model, and the analogous Ising$^*$ transitions occurring in the 3D $\mathbb{Z}_2$-gauge Higgs model, corresponding to an $N$-vector model with $N=1$. At these transitions, gauge-invariant correlations behave as in the usual $N$-vector/Ising model. Instead, the nongauge invariant spin correlations are trivial and therefore the spin order parameter that characterizes the spontaneous breaking of the O($N$) symmetry in standard $N$-vector/Ising systems is apparently absent. We define a novel gauge fixing procedure -- we name it stochastic gauge fixing -- that allows us to define a gauge-dependent vector field that orders at the transition and is therefore the appropriate order parameter for the O($N$) symmetry breaking. To substantiate this approach, we perform numerical simulations for $N=3$ and $N=1$. A finite-size scaling analysis of the numerical data allows us to confirm the general scenario: the gauge-fixed spin correlation functions behave as the corresponding functions computed in the usual $N$-vector/Ising model. The emergence of a critical vector order parameter in the gauge model shows the complete equivalence of the O($N$)$^*$/Ising$^*$ and O($N$)/Ising universality classes.

hep-lat↗

arXiv2024

The $θ$-dependence of the Yang-Mills spectrum from analytic continuation

We study the $θ$-dependence of the string tension and of the lightest glueball mass in four-dimensional $\mathrm{SU}(N)$ Yang-Mills theories. More precisely, we focus on the coefficients parametrizing the $\mathcal{O}(θ^2)$ dependence of these quantities, which we investigate by means of numerical simulations of the lattice-discretized theory, carried out using imaginary values of the $θ$ parameter. Topological freezing at large $N$ is avoided using the Parallel Tempering on Boundary Conditions algorithm. We provide controlled continuum extrapolations of such coefficients in the $N=3$ case, and we report the results obtained on two fairly fine lattice spacings for $N=6$.

hep-lat↗