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Journal of the Iranian Chemical Society

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

S. Ranjbar

Published Sep 1, 2011• 1 citation
Publisher
DOI
10.1007/bf03245918

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Using the decimation technique,a decorated square Ising lattice with two kinds of interactions K1and K2 was transformed into a regular square Ising lattice with nearest-neighbor(NN),next-nearest-neighbor(NNN),and four-spin interactions.The critical point of the approximate solution in this system was at K′C=0.4406868.The result indicated that the phase transition occurred only when the NN interaction K1 and the NNN interaction K2 satisfied a certain relation.If we only calculated the NN interaction K1,the critical point of the exact solution was at K1C=0.7635.It was also found that if we decorated two spins between the two square lattice points,the answer could be solved exactly on condition that the NN interaction existed on the doubly decorated square Ising lattice.