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Diwen wuli xuebao

CRITICAL PROPERTY TO THE ISING MODEL WITH NEXT-NEAREST-NEIGHBOR INTERACTIONS ON A DECORATED SQUARE LATTICE

Sun Chun-Feng

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Using the decimation technique,a square decorated Ising lattice with two kinds of interactionsK1andK2was transformed into a regular square Ising lattice with nearest-neighbor,next-nearest-neighbor,and four-spin interactions.The critical fixed point was found at K1C=0.5125,and K2C=0.2134,which determines the critical temperature of the system.The universality was discussed in this system.

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Using the decimation technique,a square decorated Ising lattice with two kinds of interactionsK1andK2was transformed into a regular square Ising lattice with nearest-neighbor,next-nearest-neighbor,and four-spin interactions.The critical fixed point was found at K1C=0.5125,and K2C=0.2134,which determines the critical temperature of the system.The universality was discussed in this system.
A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-neighbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2 = −0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.
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.
Abstract The static critical behavior of a 2D decorated ferromagnetic Ising model on a triangular lattice has been investigated by the methods of computational physics. For nodal spins, ferromagnetic exchange interaction between the first nearest neighbors and antiferromagnetic interaction between the next nearest neighbors have been taken into account. Exchange interaction Jd between nodal and decorated spins varies within [–3.0, 3.0]. For different values of Jd, the ground state of the model has been determined, critical temperatures have been calculated, and a phase diagram has been constructed. It has been shown that the magnitude of exchange interaction with decorated spins influences the type of phase transition to the paramagnetic state.