# A Study of the Bulk Phase Transitions of the SU(2) Lattice Gauge Theory with Mixed Action

## TL;DR

This paper re-examines the bulk phase transition in SU(2) lattice gauge theory using finite size scaling, finding no evidence of a first order transition at certain couplings and sizes, challenging previous results.

## Contribution

The study provides new finite size scaling analysis showing the absence of a first order bulk phase transition in SU(2) lattice gauge theory at specific parameters.

## Key findings

- No first order bulk phase transition observed.
- Discontinuity in average plaquette decreases with lattice size.
- Plaquette susceptibility grows slower than expected for first order.

## Abstract

Using the finite size scaling theory, we re-examine the nature of the bulk phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice gauge theory at $\beta_A = 1.25$ where previous finite size scaling investigations of the deconfinement phase transition showed it to be of first order for temporal lattices with four sites. Our simulations on $N^4$ lattices with N=6, 8, 10, 12 and 16 show an absence of a first order bulk phase transition. We find the discontinuity in the average plaquette to decrease approximately linearly with $N$. Correspondingly, the plaquette susceptibility grows a lot slower with the 4-volume of the lattice than expected from a first order bulk phase transition.