Continuous phase transitions with a convex dip in the microcanonical entropy

TL;DR

This paper investigates the convex dip in the microcanonical entropy of finite systems, revealing it can occur in continuous transitions due to finite-size effects, and develops a scaling theory to explain this phenomenon.

Contribution

The study introduces a microcanonical finite-size scaling theory for continuous phase transitions and demonstrates its validity through numerical simulations.

Findings

Convex dips can appear in continuous transitions due to finite-size effects.

The properties of these dips differ from those in first order transitions.

Numerical results support the scaling theory predictions.

Abstract

The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as for example in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.