The deconfinement phase transition in $Sp(2N)$ gauge theories and the density of states method

TL;DR

This paper investigates the deconfinement phase transition in $Sp(4)$ gauge theories using the density of states method, aiming to better understand early universe phase transitions and their gravitational wave signatures.

Contribution

It introduces a novel application of the density of states method with the linear logarithmic relaxation algorithm to study $Sp(4)$ Yang-Mills thermodynamics.

Findings

Accurate density of states determination in $Sp(4)$ gauge theory

Reconstruction of thermodynamic observables including free energy

Insights into the dynamics of the deconfinement phase transition

Abstract

First-order phase transitions in the early universe might produce a detectable background of gravitational waves. As these phase transitions can be generated by new physics, it is important to quantify these effects. Many pure Yang-Mills gauge theories are known to undergo first-order deconfinement phase transitions, with properties that can be studied with lattice simulations. Despite the recent surge of interest in $Sp(2N)$ gauge theories as a candidate for models of physics beyond the standard model, studies of these theories at finite temperature are still very limited. In this contribution we will present preliminary results of an ongoing numerical investigation of the thermodynamic properties of the deconfinement phase transition in $Sp(4)$ Yang-Mills theory, using the linear logarithmic relaxation algorithm. This method enables us to obtain a highly accurate determination of the density of states, allowing for a precise reconstruction of thermodynamic observables. In particular, it gives access to otherwise difficult to determine quantities such as the free energy of the system, even along metastable and unstable branches, hence providing an additional direct observable to study the dynamics of the phase transition.