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Criticality of the XY model in complex topologies

Miguel Ibanez Berganza, Luca Leuzzi
IPCF-CNR, UOS Roma Kerberos, Dipartimento di Fisica, Universita La Sapienza", Piazzale A. Moro, 5, 00185 Roma
arXiv:1211.3991 [cond-mat.stat-mech] (16 Nov 2012)

@article{2012arXiv1211.3991B,

   author={Berganza, Miguel Ibanez and Leuzzi, Luca},

   title={Criticality of the XY model in complex topologies},

   journal={ArXiv e-prints},

   archivePrefix={arXiv},

   eprint={1211.3991},

   primaryClass={cond-mat.stat-mech},

   keywords={Condensed Matter,Statistical Mechanics},

   year={2012},

   month={nov}

}

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The critical behavior of the O(2) model on dilute Levy graphs built on a 2D square lattice is analyzed. Different qualitative cases are probed, varying the exponent rho governing the dependence on the distance of the connectivity probability distribution. The mean-field regime, as well as the long-range and short-range non-mean-field regimes are investigated by means of high-performance parallel Monte-Carlo numerical simulations running on GPUs. The relationship between the long-range rho exponent and the effective dimension of an equivalent short-range system with the same critical behavior is investigated. Evidence is provided for the effective short-range dimension to coincide with the spectral dimension of the Levy graph for the XY model.
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