Study of two dimensional anisotropic Ising models via a renormalization group approach

Farid Taherkhani, Hamed Akbarzadeh, Hadi Abroshan, Shahram Ranjbar, Alessandro Fortunelli and Gholamabbas Parsafar

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 22, 5604-5614

Abstract: A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K=JkBT and J, kB, and T are the spin coupling interaction, the Boltzmann constant, and the absolute temperature, respectively), are calculated for different block sizes. By increasing the block size, the critical line for three types of lattice, namely: triangular, square, and honeycomb, is obtained and found to compare well with corresponding results reported by Onsager in the thermodynamic limit. Our results also show that, for the investigated lattices, there exist asymptotic limits for the critical line. Finally the critical exponents are obtained, again in good agreement with Onsager’s results. We show that the magnitude of the spin coupling interaction with anisotropic ferromagnetic characteristics does not change the values of the critical exponents, which stay constant along the direction of the critical line.

Keywords: Renormalization group; Anisotropic spin coupling interaction; 2D Ising model; Critical exponents (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:22:p:5604-5614

DOI: 10.1016/j.physa.2013.07.026

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