Ising model across planar lattices

The Ising model on a two dimensional lattice with pentagon tiling and greater number of next to neighbours interaction is equivalent to the Ising model on the centered square lattice with nearest and next to nearest neighbour non-crossing interactions. We obtain exact expressions on calculation of critical temperature with ferromagnetic and anti-ferromagnetic interactions. A direct anti-ferromagnetic bond of strength α L can give rise to the transition temperatures for appropriate α. We apply the star-triangle mapping transformation technique and decorating transform to Ising model.

Keywords: Exact results, Ising model, square lattice, transformations.  

doi:10.4038/jnsfsr.v36i4.268  

Journal of the National Science Foundation of Sri Lanka 36 (4) 303-305