Multi-body quenched disordered $XY$ and $p$-clock models on random graphs

TL;DR

This paper investigates the phase transitions and convergence properties of the disordered $XY$ and $p$-clock models on random graphs using the cavity method, revealing detailed transition lines and the effects of discretization.

Contribution

It provides a comprehensive analysis of the phase diagrams and transition lines for the $XY$ and $p$-clock models on bipartite random graphs, including convergence behavior at low temperatures.

Findings

Identification of dynamic, spinodal, and thermodynamic transition lines.

Convergence analysis of the $p$-clock model to the $XY$ model at low temperatures.

Detailed phase diagrams across different connectivities.

Abstract

The $XY$ model with four-body quenched disordered interactions and its discrete $p$-clock proxy is studied on bipartite random graphs by means of the cavity method. The phase diagrams are determined from the ordered case to the spin-glass case. Dynamic, spinodal and thermodynamic transition lines are identified by analyzing free energy, complexity and tree reconstruction functions as temperature and disorder are changed. The study of the convergence of the $p$-clock model to the $XY$ model is performed down to temperature low enough to determine all relevant transition points for different connectivity.