Long-range interactions and nonextensivity in ferromagnetic spin models

Article

关键词: RANDOM LEVY FLIGHTS;    CRITICAL-POINT;    ISING-MODEL;   

DOI  :  10.1103/PhysRevB.54.R12661

来源: SCIE

【 摘 要 】

The Ising model with ferromagnetic interactions that decay as 1/r(alpha) is analyzed in the nonextensive regime 0 less than or equal to alpha less than or equal to d, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model in the N --> infinity limit (N being the number of spins) we propose a generalization of the Curie-Weiss model, for which the N --> infinity limit is well defined for all alpha greater than or equal to 0. We conjecture that mean-field theory is exact in the last model for all 0 less than or equal to alpha less than or equal to d. This conjecture is supported by Monte Carlo heal-bath simulations in the d=1 case. Moreover, we confirm a recently conjectured scaling by Tsallis that allows for a unification of extensive (alpha>d) and nonextensive (0 less than or equal to alpha less than or equal to d) regimes.

【 授权许可】

Free