title: 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.
authors.affiliation: Research Center SMC INFM-CNR, c/o Università di Roma La Sapienza, I-00185, Roma, Italy.
authors.forename: L
authors.initials: L
authors.lastname: Angelani
authors.forename: G
authors.initials: G
authors.lastname: Ruocco