Transient backbending behavior in the Ising model with fixed magnetization

TL;DR

This paper investigates the transient backbending behavior in the caloric curve of the Ising model with fixed magnetization, revealing it as a finite-size effect that does not persist in the thermodynamic limit.

Contribution

It demonstrates that backbending is a transient finite-size phenomenon and provides criteria to distinguish between first-order transitions and finite-size effects.

Findings

Backbending is a finite-size transient behavior.

First-order transition signals include discontinuities in observables.

Backbending does not converge to a plateau in the thermodynamic limit.

Abstract

The physical origin of the backbendings in the equations of state of finite but not necessarily small systems is studied in the Ising model with fixed magnetization (IMFM) by means of the topological properties of the observable distributions and the analysis of the largest cluster with increasing lattice size. Looking at the convexity anomalies of the IMFM thermodynamic potential, it is shown that the order of the transition at the thermodynamic limit can be recognized in finite systems independently of the lattice size. General statistical mechanics arguments and analytical calculations suggest that the backbending in the caloric curve is a transient behaviour which should not converge to a plateau in the thermodynamic limit, while the first order transition is signalled by a discontinuity in other observables.