Universality and the Deconfinement Phase Transition in SU(2) Lattice Gauge Theory

TL;DR

This study uses Monte Carlo simulations to analyze the deconfinement phase transition in SU(2) lattice gauge theory, revealing a change in universality class and clarifying the nature of phase transitions at different couplings.

Contribution

It demonstrates that the deconfinement transition at non-zero temperature is first order for certain couplings and clarifies the relationship between bulk and deconfinement transitions in SU(2) lattice gauge theory.

Findings

Deconfinement transition occurs at $eta=1.20$ for $eta_A=1.1$

Transition is of first order for $eta_A extgreater= 1.1$

Bulk transition around $eta=1.33$ is actually the deconfinement transition.

Abstract

We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge theory at non-zero temperatures by Monte Carlo simulations. On an $8^3 \times 2$ lattice, at $\beta_A = 1.1$, where $\beta_A$ is the adjoint coupling, we find no evidence of any transition at the location of a previously known bulk phase transition around $\beta = 1.33$. Moreover, the deconfinement transition at $ \beta_A = 1.1$ occurs at $\beta=1.20$ and is of first order for $\beta_A \ge 1.1$, thus implying a change of universality class from that of the Wilson action at $\beta_A=0$. Computations of the plaquette susceptibility and the temporal and spatial Polyakov loops on $8^3 \times 4$ and $16^3 \times 8$ lattices at $\beta_A = 1.1$ further support these conclusions and suggest that the previously claimed bulk transition around $\beta = 1.33$ is, in fact, the first order deconfinement transition. Simulations at larger $\beta_A$ and the measurements of the mass gaps from the correlation functions of temporal and spatial Polyakov loops also confirm the temperature dependent nature of the above transition. The consequences of our results on universality are discussed.