First-order bulk transitions in large-$N$ lattice Yang--Mills theories using the density of states

TL;DR

This paper employs the LLR density of states algorithm to effectively study bulk phase transitions in large-N lattice Yang--Mills theories, overcoming traditional computational challenges and revealing insights into transition strength and latent heat.

Contribution

It introduces the LLR density of states method for analyzing bulk phase transitions in large-N lattice gauge theories, demonstrating its advantages over traditional methods.

Findings

LLR method avoids super-critical slowing down at phase transitions.

The study compares weakly and strongly first-order transitions for different N.

Results show LLR's effectiveness in analyzing large latent heat transitions.

Abstract

We use the Logarithmic Linear Relaxation (LLR) density of states algorithm to study the bulk phase transitions of pure-gauge SU($N$) lattice Yang--Mills theories with $4 \leq N \leq 8$. This approach avoids super-critical slowing down at such transitions, which poses a problem for traditional importance sampling Monte-Carlo methods. We analyse the effect of different updating strategies within the LLR algorithm, different reconstruction techniques of the density of states and different lattice volumes. By comparing our results for the weakly first-order SU(5) bulk phase transition against those for the stronger transitions with $N \geq 6$, we demonstrate the advantages of the LLR method for analyses of strong transitions with large latent heat.