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

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.

arXiv comment7 pages, 9 figures

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Cited by in corpus (5)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Energy Landscape of the Finite-Size Mean-field 3-Spin Spherical Model
• Exploring the energy landscape of XY models
• Nonlinear $XY$ and $p$-clock models on sparse random graphs: mode-locking transition of localized waves
• The topological hypothesis for discrete spin models