Universality, Lee-Yang singularities and series expansions

TL;DR

This paper presents a novel method combining Padé resummation and conformal maps to reconstruct the equation of state near a critical point from finite Taylor coefficients, focusing on the Ising universality class.

Contribution

It introduces a new approach to identify the Lee-Yang singularity and determine the critical point from limited data, applicable to models like the Gross-Neveu model.

Findings

Successfully locates the Lee-Yang edge singularity

Accurately determines the critical point and non-universal parameters

Enables numerical evaluation of the equation of state near criticality

Abstract

We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second order critical point from a finite set of Taylor coefficients computed away from the critical point. We focus on the Ising universality class (${\mathbb Z}_2$ symmetry) and show that in the crossover region of the phase diagram it is possible to efficiently extract the location of the nearest thermodynamic singularity, the Lee-Yang edge singularity, from which one can (i) determine the location of the critical point, (ii) constrain the non-universal parameters that maps the equation of state to that of the Ising model in the scaling regime, and (iii) numerically evaluate the equation of state in the vicinity of the critical point. This is done by using a combination of Pad\'e resummation and conformal maps. We explicitly demonstrate these ideas in the celebrated Gross-Neveu model.