Critical behavior of the XY model in complex topologies

Miguel Ibáñez Berganza; Luca Leuzzi

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arXiv · 1211.3991

Critical behavior of the XY model in complex topologies

Miguel Ibáñez Berganza·Luca Leuzzi

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Abstract

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 in the mean-field regime.

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Miguel Ibáñez Berganza, Luca Leuzzi. 2013-08-15. Critical behavior of the XY model in complex topologies. https://arxiv.org/abs/1211.3991

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