Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

TL;DR

This paper investigates one-dimensional models with nearest neighbor interactions that display pseudo-phase transitions, characterized by sharp but non-true phase transition behaviors, analyzed through derivatives of free energy and correlation length.

Contribution

It identifies conditions under which quasi-phases and pseudo-transitions occur in one-dimensional models, clarifying their distinguishing features from true phase transitions.

Findings

Pseudo-transitions mimic first and second order phase transitions.

Sharp peaks in specific heat and susceptibility at pseudo-critical temperatures.

Correlation length peaks confirm pseudo-transition phenomena.

Abstract

There are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of chain structures, which exhibit unexpected behaviors quite similar to the first and second order phase transition, which could be confused naively with an authentic phase transition. Through the analysis of the first derivative of free energy, such as entropy, magnetization, and internal energy, a "sudden" jump that closely resembles a first-order phase transition at finite temperature occurs. However, by analyzing the second derivative of free energy, such as specific heat and magnetic susceptibility at finite temperature, it behaves quite similarly to a second-order phase transition exhibiting an astonishingly sharp and fine peak. The correlation length also confirms the evidence of this pseudo-transition temperature, where a sharp peak occurs at the pseudo-critical temperature. We also present the necessary conditions for the emergence of these quasi-phases and pseudo-transitions.