J. Iran. Chem. Soc., Vol. 8, No. 3 September 2011, pp.872~878.

Current location: JICS Archive > Vol. 8 > No. 3 > Articles : 28

# The Exact Determination of the Critical Points for 2-D Square Lattice Ising Model with the Nearest and Next Nearest Neighbors Interactions

*S. Ranjbar*

### Chemistry Department, Science College,Razi University, Kermanshah, Iran

The combinatorial factor method (CFM)** **was used to find the critical points of the 2-D square lattice Ising model with the nearest neighbor (with the coupling constant *J*_{nn}) and the next nearest neighbor (with the coupling constant *J*_{nnn}) interactions. In the absence of the magnetic field, for the various values of coupling ratio, *α* = *J*_{nnn}/*J*_{nn} (0 ≤ *α* < 1), the exact values of * j*_{c} (= *J*_{nn}/*kT*_{c}) were obtained. Finally, based on such values, an analytical expression for the *j*_{c} as a function of *α *has been proposed

**Keywords:** Ising model, Combinatorial factor, Phase transition, Nearest- and next nearest-neighbors