Absence of phase transitions in self-dual Ising models with multisite interactions and a field

Abstract

The author investigates Ising spin systems having a single translationally invariant multispin interaction and an external magnetic field. These models are self-dual and for certain intervals of the self-dual line Heringa, Blote and Hoogland have very recently obtained by Monte Carlo simulations evidence for a first-order phase transition. He finds intervals of the self-dual line where one can rigorously prove the absence of a phase transition (these areas do not contradict the Monte Carlo results). He does this by looking at the zeros of the partition function.