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

•There is a good agreement for critical exponent of 2-D anisotropic of Ising model with Onsager’s results.•Critical exponents remain constant versus ferromagnetic anisotropic spin coupling interaction.•There is an asymptotic limit for the critical line.

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, KsKs (where K=JkBT and JJ, kBkB, and TT 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.