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 regul...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-nelghbor, 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.展开更多
Using Monte Carlo method with zero-temperature dynamics, we investigate energy evolution of Ising spin configuration on a square lattice. The energies of some configurations exhibit long duration before those configur...Using Monte Carlo method with zero-temperature dynamics, we investigate energy evolution of Ising spin configuration on a square lattice. The energies of some configurations exhibit long duration before those configurations reach the final state -- ground state or frozen stripe state. For ground-state dynamical realization, the duration occurs when the energy per spin is 4/L, where L is the lattice size. For stripe-state dynamical realization, the energy is slightly higher than 2/L when the duration appears in the last evolution stage. In addition, it is found that the average energy per spin in final state is approximately 2/3L.展开更多
Two catalyzed-birth models of n-species （n ≥ 2） aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Ak^m and Af^m of...Two catalyzed-birth models of n-species （n ≥ 2） aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Ak^m and Af^m of the same species with the rate kernels Km（k,j）= Kmkj （m = 1, 2,... ,n, n ≥ 2）, and aggregates of A^n species catalyze a monomer-birth of A^l species （l = 1, 2 , n - 1） with the catalysis rate kernel Jl（k,j） -Jlkj^v. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution ak^l（t） of A^l species depends crucially on the value of the catalysis rate parameter v： （i） ak^l（t） obeys the conventional scaling law in the case of v ≤ 0, （ii） ak^l（t） satisfies a modified scaling form in the case of v 〉 0. In the second model, the mechanism of monomer-birth of An-species catalyzed by A^l species is added on the basis of the first model, that is, the aggregates of A^l and A^n species catalyze each other to cause monomer-birth. The kinetic behaviors of A^l and A^n species are found to fall into two categories for the different v： （i） growth obeying conventional scaling form with v ≤ 0, （ii） gelling at finite time with v 〉 0.展开更多
The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian.distribution constants b and bw is constructed by generalizing that on tra...The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian.distribution constants b and bw is constructed by generalizing that on translationally invariant square lattice.The critical behaviours are studied by the renormalization-group approach and spin rescaling method.They are found to be quite different from that on translationally invariant square lattice.There are two critical points at(K^(*)=b,K^(*)_(w)=0)and(K^(*)=0,K^(*)_(w)=bw),and the correlation length critical exponents are calculated.展开更多
基金The project supported by the Natural Science Foundation of Xiaogan University and the Science Foundation of Qufu Normal University
文摘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-nelghbor, 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.
文摘Using Monte Carlo method with zero-temperature dynamics, we investigate energy evolution of Ising spin configuration on a square lattice. The energies of some configurations exhibit long duration before those configurations reach the final state -- ground state or frozen stripe state. For ground-state dynamical realization, the duration occurs when the energy per spin is 4/L, where L is the lattice size. For stripe-state dynamical realization, the energy is slightly higher than 2/L when the duration appears in the last evolution stage. In addition, it is found that the average energy per spin in final state is approximately 2/3L.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10275048 and 10305009 and the Natural Science Foundation of Zhejiang Province of China under Grant No. 102067
文摘Two catalyzed-birth models of n-species （n ≥ 2） aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Ak^m and Af^m of the same species with the rate kernels Km（k,j）= Kmkj （m = 1, 2,... ,n, n ≥ 2）, and aggregates of A^n species catalyze a monomer-birth of A^l species （l = 1, 2 , n - 1） with the catalysis rate kernel Jl（k,j） -Jlkj^v. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution ak^l（t） of A^l species depends crucially on the value of the catalysis rate parameter v： （i） ak^l（t） obeys the conventional scaling law in the case of v ≤ 0, （ii） ak^l（t） satisfies a modified scaling form in the case of v 〉 0. In the second model, the mechanism of monomer-birth of An-species catalyzed by A^l species is added on the basis of the first model, that is, the aggregates of A^l and A^n species catalyze each other to cause monomer-birth. The kinetic behaviors of A^l and A^n species are found to fall into two categories for the different v： （i） growth obeying conventional scaling form with v ≤ 0, （ii） gelling at finite time with v 〉 0.
基金Supported by the Foundation of“151 Talent Engineering”of Zhejiang Province,and the Foundation of“551 Talent Engineering”of Wenzhou City of China.
文摘The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian.distribution constants b and bw is constructed by generalizing that on translationally invariant square lattice.The critical behaviours are studied by the renormalization-group approach and spin rescaling method.They are found to be quite different from that on translationally invariant square lattice.There are two critical points at(K^(*)=b,K^(*)_(w)=0)and(K^(*)=0,K^(*)_(w)=bw),and the correlation length critical exponents are calculated.
