Equation of state near the endpoint of the critical line

TL;DR

This paper investigates the critical behavior near the endpoint of the critical line in systems within the Ising universality class, using non-perturbative flow equations to connect microscopic properties with universal features of the equation of state.

Contribution

It introduces a non-perturbative flow equation approach to analyze the critical endpoint, providing direct access to universal features without relying on scaling assumptions.

Findings

Universal features match well with other methods

Short distance physics can be inferred from the endpoint location

Method avoids perturbative series resummation

Abstract

We discuss first order transitions for systems in the Ising universality class. The critical long distance physics near the endpoint of the critical line is explicitly connected to microscopic properties of a given system. Information about the short distance physics can therefore be extracted from the precise location of the endpoint and non-universal amplitudes. Our method is based on non-perturbative flow equations and yields directly the universal features of the equation of state, without additional theoretical assumptions of scaling or resummations of perturbative series. The universal results compare well with other methods.