Emergence of a non trivial fluctuating phase in the XY model on regular networks

Sarah de Nigris (1) , Xavier Leoncini (1)

1 CPT - Centre de Physique Théorique - UMR 7332

We study the XY model on diluted networks. Considering the regular one-dimensional lattice topology, we focus on the influence of the dilution parameter 2>gamma>1. We find that for gamma<1.5,
the system does not exhibit a phase transition, while for gamma>1.5 a second order transition of the magnetisation arises and displays identical properties as the mean field (HMF) regime. Hence gamma(c)=1.5 appears to be a critical value, for which, in an identified energy range, the magnetisation shows important fluctuations. We resort to analytical calculations of the magnetisation in the low temperatures approximation regime and we show that our analytics breaks down below the threshold of gamma(c) while it gives the correct value above,
confirming the critical value gamma(c)=1.5.

Mots clés: XY model; regular network; hamiltonian chaos; statistical mechanics; spin models

Domaines: Mécanique statistique [cond-mat.stat-mech]

Sarah de Nigris, Xavier Leoncini. Emergence of a non trivial fluctuating phase in the XY model on regular networks. 2012. ⟨hal-00721437v1⟩