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

Taherkhani, F ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1016/j.physa.2013.07.026
  3. Publisher: 2013
  4. Abstract:
  5. 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=J/kBT 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
  6. Keywords:
  7. 2D Ising model ; Anisotropic spin coupling interaction ; Critical exponents ; Renormalization group ; Anisotropic spin couplings ; Critical exponent ; Nearest-neighbor interactions ; Real-space renormalization group ; Renormalization group approach ; Thermodynamic limits ; Ising model ; Statistical mechanics ; Two dimensional ; Anisotropy
  8. Source: Physica A: Statistical Mechanics and its Applications ; Volume 392, Issue 22 , 2013 , Pages 5604-5614 ; 03784371 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0378437113006365