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Phase transitions in center-stabilized lattice gauge theories

Helvio Vairinhos

TL;DR

This work investigates center-stabilized lattice gauge theories (deformed YM, $dYM$) on $\mathbb{R}^3\times S^1$ to realize large-$N$ volume independence. It introduces a Hubbard-Stratonovich-based pseudo-heatbath algorithm that linearizes the deformation terms and efficiently updates the compact-direction links, enabling nonperturbative exploration of phase structure. For $N=4,5$ on a $6^3 1$ lattice, it maps phase diagrams as functions of the lattice coupling and deformation parameters, identifying confining, deconfining, and partially confining regimes governed by the $Z_N$ center symmetry; full preservation of $Z_N$ yields an equivalence to YM on $\mathbb{R}^4$ up to $O(1/N^2)$ corrections, with partial breaking when certain deformations are insufficient. The results support Ünsal–Yaffe predictions for critical deformation values $a_{n,c}=4/(\pi^2 n^2)$ and demonstrate the feasibility of volume reduction with appropriate deformations in the large-$N$ limit.

Abstract

We simulate four-dimensional center-stabilized lattice Yang-Mills theories on R^3 x S^1 with a newly developed pseudo-heatbath algorithm. We analyze the phase structure of such theories, namely the bulk transition and the spontaneous breaking of the center symmetry associated with the compact direction.

Phase transitions in center-stabilized lattice gauge theories

TL;DR

This work investigates center-stabilized lattice gauge theories (deformed YM, ) on to realize large- volume independence. It introduces a Hubbard-Stratonovich-based pseudo-heatbath algorithm that linearizes the deformation terms and efficiently updates the compact-direction links, enabling nonperturbative exploration of phase structure. For on a lattice, it maps phase diagrams as functions of the lattice coupling and deformation parameters, identifying confining, deconfining, and partially confining regimes governed by the center symmetry; full preservation of yields an equivalence to YM on up to corrections, with partial breaking when certain deformations are insufficient. The results support Ünsal–Yaffe predictions for critical deformation values and demonstrate the feasibility of volume reduction with appropriate deformations in the large- limit.

Abstract

We simulate four-dimensional center-stabilized lattice Yang-Mills theories on R^3 x S^1 with a newly developed pseudo-heatbath algorithm. We analyze the phase structure of such theories, namely the bulk transition and the spontaneous breaking of the center symmetry associated with the compact direction.

Paper Structure

This paper contains 4 sections, 10 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Monte Carlo algorithm
  3. Phase structure
  4. Conclusions

Figures (4)

  • Figure 1: Reduced Polyakov loop wrapping the compact direction of ${\mathbb{R}^3\times S^1}$.
  • Figure 2: Estimator of the autocorrelation function ($C$) vs. CPU time ($t_{\rm CPU}$) in simulations of $SU(5)$ dYM theory on a $10^3 1$ lattice, with $\lambda^{-1}=0.5$ and $(a_1, a_2)=(0.20, 0.05)$ (left), and the corresponding estimator of the integrated autocorrelation time ($\tau_{\rm int}$) vs. Monte Carlo time ($t$) (right). We compared a Cabibbo-Marinari-Metropolis algorithm for dYM (red) with the pseudo-heatbath algorithm described in the text (blue).
  • Figure 3: Phase diagrams on the $(\lambda^{-1},a_1)$ plane of $SU(4)$ dYM on a $6^3 1$ lattice, for vanishing double-winding deformation (left) and large double-winding deformation (right).
  • Figure 4: Phase diagrams on the $(\lambda^{-1},a_1)$ plane of $SU(5)$ dYM on a $6^3 1$ lattice, for vanishing double-winding deformation (left) and large double-winding deformation (right).