Universality, Lee-Yang singularities and series expansions

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.