# Density of partition function zeroes and phase transition strength

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0117.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**Density of partition function zeroes and phase transition strength**

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 efficiacy 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.