Phys. Rev. B 54, R12661 - R12664 (1996)Long-range interactions and nonextensivity in ferromagnetic spin models |
Sergio A. Cannas * and Francisco A. Tamarit †
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Haya de la Torre y Medina Allende S/N, Ciudad Universitaria, 5000 Córdoba, Argentina
Received 26 December 1995; revised 29 July 1996
The Ising model with ferromagnetic interactions that decay as 1 / rα is analyzed in the nonextensive regime 0<~α<~d, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model in the N→∞ limit (N being the number of spins) we propose a generalization of the Curie-Weiss model, for which the N→∞ limit is well defined for all α>~0. We conjecture that mean-field theory is exact in the last model for all 0<~α<~d. This conjecture is supported by Monte Carlo heat-bath simulations in the d=1 case. Moreover, we confirm a recently conjectured scaling by Tsallis that allows for a unification of extensive (α>d) and nonextensive (0<~α<~d) regimes.
©1996 The American Physical Society
URL: http://link.aps.org/abstract/PRB/v54/pR12661
DOI: 10.1103/PhysRevB.54.R12661
* Member of the Nacional Research Council, CONICET (Argentina). Also at Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janiero, Brazil. Electronic address: cannas@fis.uncor.edu
† Also at Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janiero, Brazil. Electronic address: tamarit@fis.uncor.edu
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