The critical behavior of the O(2) model on dilute Lévy graphs built on a two-dimensional square lattice is analyzed. Different qualitative cases are probed, varying the exponent ρ 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 ρ 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 Lévy graph for the XY model in the mean-field regime. © 2013 American Physical Society.

Critical behavior of the XY model in complex topologies

Ibáñez Berganza M.;
2013-01-01

Abstract

The critical behavior of the O(2) model on dilute Lévy graphs built on a two-dimensional square lattice is analyzed. Different qualitative cases are probed, varying the exponent ρ 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 ρ 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 Lévy graph for the XY model in the mean-field regime. © 2013 American Physical Society.
File in questo prodotto:
File Dimensione Formato  
1211.3991.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 1.3 MB
Formato Adobe PDF
1.3 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/24998
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
social impact