Partition Function Zeroes

The study of phase transitions is central to statistical mechanics. Of primary interest is the determination of the location, the order and the strength of the transitions. Going from finite sized systems, as in lattice simulations, to the thermodynamic limit using finite size scaling is a well established way of estimating critical exponents and temperatures. An alternative approach, pioneered by Lee and Yang for field-driven transitions and Fisher for temperature-driven transitions, is to consider the partition function of a finite system as a polynomial and study the properties of its zeroes as the system size is increased. In the talk we look at such ''partition function zeroes'' and discuss their advantages and disadvantages for studying phase transitions.