Deconfinement and universality in the 3D U(1) lattice gauge theory at finite temperature: study in the dual formulation

O Borisenko,A Papa,M Gravina,V Chelnokov

doi:10.1007/jhep09(2015)062

Abstract

We study analytically and numerically the three-dimensional U(1) lattice gauge theory at finite temperature in the dual formulation. For an appropriate disorder operator, we obtain the renormalization group equations describing the critical behavior of the model in the vicinity of the deconfinement phase transition. These equations are used to check the validity of the Svetitsky-Yaffe conjecture regarding the critical behavior of the lattice U(1) model. Furthermore, we perform numerical simulations of the model for N t = 1, 2, 4, 8 and compute, by a cluster algorithm, the dual correlation functions and the corresponding second moment correlation length. In this way we locate the position of the critical point and calculate critical indices.

Highlights

The critical points and the index η in the Villain formulation of finite-temperature 3D U(1) have been determined for various values of Nt in [8], via numerical analysis of the RG equations, confirming that η = 1/4
JHEP09(2015)062 where t = βc/β − 1, the correlation length goes as ξ ∼ ebt−ν, and the critical index ν is equal to 1/2 in 2D XY
Evidences that the deconfinement transition in the 3D U(1) LGT belongs to the universality class of the 2D XY model come from our study of the phase transitions in 3D Z(N ) LGT [9,10,11,12,13] for large values of N

Summary

Introduction

The critical points and the index η in the Villain formulation of finite-temperature 3D U(1) have been determined for various values of Nt in [8], via numerical analysis of the RG equations, confirming that η = 1/4. Calculate the disorder operator in the dual formulations of the 2D XY spin model and in the 3D U(1) LGT in the dilute gas approximation.

Results

Conclusion