Mixed order transition and condensation in exactly soluble one dimensional spin model

TL;DR

This paper analyzes an exactly solvable one-dimensional spin model exhibiting mixed order phase transitions, exploring its properties in different ensembles, generalizations, and broader interaction classes to deepen understanding of MOT phenomena.

Contribution

It extends previous work by analyzing the model in the canonical ensemble and generalizing it to Potts and Ising spins with various power-law interactions.

Findings

The model exhibits mixed order phase transitions with both discontinuous order parameters and diverging correlation lengths.

Canonical ensemble analysis provides new insights into the transition mechanism.

Generalizations to Potts and Ising spins with different decay exponents broaden the applicability of the model.

Abstract

Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far from thermal equilibrium. In a recent paper [1] an exactly soluble spin model with long-range interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to lay a bridge between two classes of one dimensional models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper we elaborate on the calculations done in [1]. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins, and also consider a broader class of interactions which decay with distance with a power law different from 2.