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

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.

15 pages, 6 figures

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Cited by in corpus (8)

• Approximating the XY model on a random graph with a $q$-state clock model
• Self-starting nonlinear mode-locking in random lasers
• The low-temperature phase in the two-dimensional long-range diluted XY model
• Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models
• Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs
• Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables
• Inverse problem for multi-body interaction of nonlinear waves
• Critical properties of disordered XY model on sparse random graphs