# Deconfinement transition and dimensional cross-over in the 3D gauge Ising model

## TL;DR

This study uses high-precision Monte Carlo simulations to analyze the deconfinement transition in a 3D Z2 gauge theory, confirming the Svetitsky-Yaffe conjecture and exploring dimensional crossover effects.

## Contribution

It provides highly accurate critical temperature and exponent data for the 3D Z2 gauge theory, validating theoretical predictions and examining dimensional crossover phenomena.

## Key findings

- Critical temperature matches 3D Ising model results
- Critical exponents confirm Svetitsky-Yaffe conjecture
- Deviations from Olesen's prediction are around 20%

## Abstract

We present a high precision Monte Carlo study of the finite temperature $Z_2$ gauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows us to use powerful cluster algorithms for the simulations. For temporal extensions up to $N_t=16$ we obtain the inverse critical temperature with a statistical accuracy comparable with the most accurate results for the bulk phase transition of the 3D Ising model. We discuss the predictions of T. W. Capehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions. Our precise data for the critical exponents and critical amplitudes confirm the Svetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the critical temperature of about 20%.