Exact microcanonical statistical analysis of transition behavior in Ising chains and strips

TL;DR

This paper performs an exact microcanonical analysis of the Ising model in one and quasi-one dimensions, revealing transition signals in strips but not in chains, enhancing understanding of phase transition signatures in low-dimensional systems.

Contribution

It provides a detailed microcanonical analysis of the Ising chain and strips, identifying transition features as strip width increases, which was not previously characterized in detail.

Findings

Transition signals emerge in strips with increasing width.

No transition signals are found in the one-dimensional chain.

Analysis enhances understanding of low-dimensional phase transitions.

Abstract

Recent analyses of least-sensitive inflection points in derivatives of the microcanonical entropy for the two-dimensional Ising model revealed higher-order transition signals in addition to the well-studied second-order ferromagnetic/paramagnetic phase transition. In this paper, we re-analyze the exact density of states for the one-dimensional Ising chain as well as the strips with widths/lengths of up to 64/1024 spins, in search of potential transition features. While some transitions begin to emerge as the strip width increases, none are found for the chain, as might be expected.