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

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.