Diwen wuli xuebao

THE APPROXIMATE SOLUTION TO THE ISING MODEL ON A DECORATED SQUARE LATTICE

Xiang-Mu Kong

Published Jan 1, 2010• 0 citations

Abstract

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.

Related papers

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

Sun Chun-Feng

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.

Diwen wuli xuebaoJan 1, 20120 citations

A Solvable Decorated Ising Lattice Model

Sun Chun-Feng, Xiang-Mu Kong, Xun-Chang Yin

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.

Communications in Theoretical PhysicsMar 1, 20069 citations

AN APPROXIMATE SOLUTION FOR SQUARE-LATTICE SPIN-1 MODEL

YE QING, 上海交通大学应用物理系凝聚态物理研究所

In this paper, we apply the decoration and decimation transformation to the square-lattice spin-1 model and show that it is equivalent toa checkerboard Ising model with cross and four-spin interactions. Then, the approximate critical condition is obtained for the model and it reduces to Onsager's exact solution in the Ising-model limit.

Acta Physica SinicaJan 1, 19890 citations

The phase diagram of the Gauss model on a decorated square lattice

Sun Chun-Feng

Using equivalent transformation and spin-rescaling methods, the Gauss model on a decorated square lattice is studied. It is found that the square decorated Gauss lattice could be transformed into a regular square Gauss lattice with nearest-neighbor, and next-nearest-neighbor interactions. By calculating the regular square-lattice Gauss model, the critical temperature of the Gauss model is obtained on a decorated square lattice, and the exact phase diagram of this system can also be obtained.

Acta Physica SinicaJan 1, 20120 citations

Phase diagram and critical exponent ν for the nearest-neighbor and next-nearest-neighbor interaction Ising model

James L. Monroe, Seung‐Yeon Kim

We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent nu. Our results are compared to previous results for this system using a wide variety of other approaches.

Physical Review EAug 29, 200730 citations

Phase Diagram and the Ground State of the Decorated Ising Model on a Triangular Lattice with Ferromagnetic Interaction between the First Nearest Neighbors and Antiferromagnetic Interaction between the Next Nearest Neighbors

Vadim A. Mutailamov, Akai Kurbanovich Murtazaev

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.

Journal of Experimental and Theoretical PhysicsDec 1, 20225 citations