Density of Partition Function Zeroes and Phase Transition Strength

Abstract

A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase transitions numerically. Furthermore, it enables efficient distinguishing between first and second order transitions, elucidates crossover between them and illuminates the origins of finite-size scaling. The efficacy of the technique is demonstrated by its application to a number of models in the case of Fisher zeroes and to the XY model in the case of Lee-Yang zeroes.