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

TL;DR

The paper investigates the finite-temperature deconfinement transition and dimensional crossover in the 2+1D $Z_2$ gauge theory by exploiting the exact duality to the 3D Ising spin model and performing high-precision Monte Carlo simulations up to $N_t=16$. Using a cluster algorithm and a dynamic boundary-condition observable $Z_{ap}/Z_p$, the authors test the Svetitsky–Yaffe conjecture and the Capehart–Fisher dimensional-crossover framework, obtaining precise critical temperatures and exponents. They confirm the SY universality, finding $\nu\approx0.628$ and $\eta\approx0.25$ in agreement with the 2D Ising universality, and they measure $T_c/\sqrt{\sigma}$ to test the Olesen conjecture, obtaining $1.2216(24)$ which deviates from the bosonic-string prediction by about 20%. The results also support a dimensional crossover exponent $\lambda=1/\nu\approx0.63$ for periodic boundary conditions. Together, the findings solidify the link between deconfinement, dimensional crossover, and effective string descriptions in this minimal lattice gauge theory setting and provide high-precision benchmarks for related methods.

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%.