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

Centre de Physique Théorique, CNRS - Aix-Marseille Université - Luminy, Case 907, F-13288 Marseille cedex 9, France, EU

Received: 28 September 2012
Accepted: 11 December 2012

Abstract

We study an XY-rotor model on regular one-dimensional lattices by varying the number of neighbours. The parameter 2 ⩾ γ ⩾ 1 is defined. γ = 2 corresponds to mean field and γ = 1 to nearest-neighbours coupling. We find that for γ < 1.5 the system does not exhibit a phase transition, while for γ > 1.5 the mean-field second-order transition is recovered. For the critical value γ = γ_c = 1.5, the systems can be in a non-trivial fluctuating phase for which the magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibilty. For all values of γ the magnetisation is computed analytically in the low-temperatures range and the magnetised vs. non-magnetised states are recovered, confirming the critical value γ_c = 1.5.