Unveiling phase transitions in 1D systems with short-range interactions

TL;DR

This paper demonstrates that a 1D Ising model with short-range interactions can exhibit a finite-temperature phase transition when using an appropriate order parameter, combining analytical and simulation methods.

Contribution

It shows that selecting the magnetization modulus as the order parameter reveals a phase transition in 1D systems, challenging traditional beliefs.

Findings

Detected a phase transition at ~15 K in the 1D Ising model

Analytical and high-precision simulations confirm the transition

Proper order parameter choice is crucial for observing phase transitions

Abstract

The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. To accomplish this, we combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely the module of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that an inappropriate choice of the order parameter may mask phase transitions in one-dimensional systems.