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Palma G, Meyer T, Labbé R. Finite size scaling in the two-dimensional XY model and generalized universality. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;66(2):026108doi: 10.1103/PhysRevE.66.026108.
Palma, G., Meyer, T., & Labbé, R. (2002). Finite size scaling in the two-dimensional XY model and generalized universality. Physical review. E, Statistical, nonlinear, and soft matter physics, 66(2), 026108. https://doi.org/10.1103/PhysRevE.66.026108
Palma, G, et al. "Finite size scaling in the two-dimensional XY model and generalized universality." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 66,2 (2002): 026108. doi: https://doi.org/10.1103/PhysRevE.66.026108
Palma G, Meyer T, Labbé R. Finite size scaling in the two-dimensional XY model and generalized universality. Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Aug;66(2):026108. doi: 10.1103/PhysRevE.66.026108. Epub 2002 Aug 16. PMID: 12241238.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Aug;66(2):026108. doi: 10.1103/PhysRevE.66.026108. Epub 2002 Aug 16.

Finite size scaling in the two-dimensional XY model and generalized universality.

Physical review. E, Statistical, nonlinear, and soft matter physics

G Palma, T Meyer, R Labbé

Affiliations

  1. Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile.

PMID: 12241238 DOI: 10.1103/PhysRevE.66.026108

Abstract

In recent works [S. T. Bramwell, P. C. W. Holdsworth, and J.-F. Pinton, Nature (London) 396, 552 (1998); S. T. Bramwell et al., Phys. Rev. Lett. 84, 3744 (2000)], a generalized universality has been proposed, linking phenomena as dissimilar as two-dimensional (2D) magnetism and turbulence. To test these ideas, we performed Monte Carlo simulations of the 2D XY model. We found that the shape of the probability distribution function for the magnetization M is non-Gaussian and independent of the system size-in the range of the lattice sizes studied-below the Kosterlitz-Thoules temperature. However, our results suggest that in the full 2D XY model the shape of these distributions has a slight dependence on temperature-for finite volume-below the lattice-shifted critical temperature T*(L). This behavior can be explained by using renormalization group arguments and an extended finite-size scaling analysis, and by the existence of bounds for M.

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