Critical Behavior Of Ising Model Research Articles

Critical behavior of ising models with random long-range (small-world) interactions

The critical scaling behavior of Ising models with long range interactions is studied. These long-range interactions, when imposed in addition to interactions on a regular lattice, lead to small world graphs. Large-scale Monte Carlo simulations, together with finite-size scaling, is used to obtain the critical behavior of a number of different models. These include the z-model introduced by Scalettar, standard small-world bonds superimposed on a square lattice, and physical small-world bonds superimposed on a square lattice. These scaling results provide further evidence to support the existence of physical (quasi-) small-world nanomaterials.

Behavior of a wetting phase near a solid boundary: vapor near a weakly attractive surface

Density profiles of a LJ vapor near a weakly attractive surface with long-range fluid wall potential was studied along the pore coexistence curve. There are two localized density maxima near the pore wall: the first one is caused by localization of the molecules in the minimum of the fluid-wall potential, and the second one reflects adsorption of molecules at the first layer at higher densities. In addition, a third, weak density maximum is observed close to the critical temperature due to the competition between the long-range attractive tail of the fluid-wall potential and the effect of missing neighbors. This maximum separates the region of a gradual density depletion toward the surface due to the missing neighbor effect and the adsorption region further from the surface, where the density gradually increases toward the surface due to the attractive fluid-wall potential. When approaching the bulk critical temperature, this maximum moves away from the surface due to the divergence of the bulk correlation length. Applicability of various equations to describe the vapor density profiles is examined. Excess adsorption of vapor at low temperatures turns into excess depletion at higher temperatures. The crossover temperature increases with increasing pore size and strengthening fluid-wall interaction. The problems of the theory of the surface critical behavior of Ising models in a case of a non vanishing surface field and its mapping on a fluid is discussed.

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities**The project supported by National Natural Science Foundation of China under Grant No. 10275014

The theoretic renormalization-group approach is applied to the study of the critical behavior of the -dimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations . The asymptotic scaling law is studied in the framework of the expansion in . In , the dynamic exponent is calculated up to the second order in with . The shape function is obtained in one-loop calculation. When , the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.

Ising model on the edge-dual of random networks.

We consider the Ising model on the edge dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High- and low-temperature expansions of Ising model on the edge dual of random networks are derived. A detailed comparison of the critical behavior of Ising model on scale free random networks and their edge dual is presented.

The Critical Behavior of the Ising Model on Union Jack Lattice11The project supported by Science Foundation of Shanghai Jiaotong University

In this paper, we have investigated the critical behavior of the ferromagnetic Ising model on union jack lattice. The model is equivalent to the eight-vertex model which can be solved as a free fermion model with the free fermion approximation. The critical exponents have been obtained as and .

Transfer matrix studies of d≥3 Ising models

A novel numerical transfer matrix approach to obtain the critical behavior of Ising models in dimensions higher than two is described. The approach augments the physical transfer matrices with other matrices which do not necessarily have a straightforward physical interpretation. These additional matrices have approximately the same form as the physical transfer matrices, and for high dimensions may provide the only way of performing finite size scaling using transfer matrix calculations. Results are presented for the Ising model in three, four, and five dimensions.

CRITICAL BEHAVIOUR OF ISING MODEL WITH THREE-SPIN INTERACTIONS ON THREE-NODE HIERARCHICAL LATTICES

The critical behavior of Ising model with three-spin interactions on three-node hierarchical lattices is investigated by using an exact renormalization group transformation. As in the case of Bravais lattices, the model with two-spin interactions and the one with three-spin interactions belong to different universality classes.

Critical behavior of Ising models with static site dilution.

Critical behavior of Ising models with static site dilution.