Finite-size scaling of partition function zeros and first-order phase transition for infinitely long Ising cylinder

TL;DR

This paper investigates the finite-size effects on the partition function zeros of an infinitely long Ising strip with finite width, revealing a first-order phase transition under antiperiodic boundary conditions and providing exact scaling relations.

Contribution

It provides exact finite-size scaling laws for partition function zeros and identifies a first-order transition with quantifiable latent heat for antiperiodic boundary conditions.

Findings

Partition function zeros follow specific finite-size scaling laws.

Antiperiodic boundary conditions induce a first-order phase transition.

Latent heat of transition is exactly 4/L.

Abstract

The critical properties of an infinitely long Ising strip with finite width L joined periodically or antiperiodically are investigated by analyzing the distribution of partition function zeros. For periodic boundary condition, the the leading finite-size scaling of partition function zeros and its corrections are given. For antiperiodic boundary condition, the critical point of 2D Ising transition is one of the loci of the zeros, and the associated non-analyticity is identified as a first-order phase transition. The exact amount of the latent heat released by the transition is 4/L.