Mixed-order phase transition in a minimal, diffusion based spin model

TL;DR

This paper presents an exact solution of a minimal diffusion-based spin model exhibiting a hybrid phase transition characterized by a mix of first- and second-order transition features, including a triple point with diverging susceptibilities.

Contribution

The paper introduces a minimal, exactly solvable spin model with a hybrid phase transition, linking dynamic procedures to equilibrium statistical mechanics.

Findings

Identified a triple point with hybrid transition features

Derived the phase diagram showing mixed-order behavior

Demonstrated algebraic divergence of susceptibilities at the triple point

Abstract

In this paper, we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model "diffusion-based" because its hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.