Phase transitions and topology in 2+k XY mean-field models

TL;DR

This paper investigates the relationship between phase transitions and topological changes in mean-field XY models with multi-body interactions, revealing that topological changes occur at phase transitions but do not always indicate their order.

Contribution

It introduces a detailed analysis of thermodynamic and topological properties in 2+k XY mean-field models, highlighting the complex relationship between topology and phase transitions.

Findings

Topological change occurs at the phase transition energy.

Only one topological change is observed even with multiple phase transitions.

Topological curvature does not fully indicate the order of phase transitions.

Abstract

The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase transition energy, thermodynamically forbidden energy regions) and topological (singularity and curvature of saddle entropy) properties is performed. We find that i) a topological change is present at the phase transition energy; however, ii) only one topological change occurs, also for those models exhibiting two phase transitions; iii) the order of a phase transition is not completely signaled by the curvature of topological quantities.