A One-Dimensional System Undergoing First-Order Diffuse Phase Transition

Abstract

A one-dimensional lattice gas with repulsive potential u₁>0 between nearest neighbors and attractive potential u₂<0 between second neighbors is discussed. In the limit of u₁, |u₂|→∞ while keeping u₁+u₂=finite<0, a phase transition is expected. However, in the case when both u₁ and |u₂| are finite but large, a diffuse phase transition is obtained. This model is regarded as a lattice gas version of the helix-coil transition in polypeptides. The distribution of the zeroes of the grand partition function is also discussed through computer calculation.