Miguel  Berganza, IPCF-CNR Roma #
Criticality of continuous spin models in random graphs. A Monte-Carlo
parallel algorithm in GPUs. #
We have developed a parallel GPU-based Monte-Carlo algorithm devoted to
the analysis of continuous spin models in disordered graphs. This tool
facilitates the study of the critical behaviour of the XY model on a Levy
graph, such that the bond probability decays as a power, rho, of the
distance between bonds with respect to their position in a given
(short-range) lattice. Varying rho from infinity to zero, the Levy graph
interpolates between the lattice and the uncorrelated (Erdos-Rany) graph.
Renormalization group arguments allow to define three regimes of rho in
correspondence with different critical behaviours of the model: for
sufficiently low rho the model presents a phase transition of the
mean-field type, whether for large values of rho the transition is
supposed to belong to the Kosterlitz-Thouless universality class. We 
provide numerical support of these results, which are in agreement with 
previous
studies of the XY model in complex topologies (Cassi, Phys. Rev. Lett. 68
3631 (1992)). Our research is motivated by the study of continuous spin
models with disordered, long-range interactions, relevant in the
statistical description of modes in random lasers (Conti and Leuzzi Phys.
Rev. E 83 134204 (2011)).