A proof is presented to show that there exists no spontaneous magnetization at high temperatures for the Ising model on the square lattice when the interactions are between nearest-neighbour pairs as well as between quartets on the basic plaquettes. The proof can be extended to the general Ising...

The existence of the thermodynamic limit is proved for the random one-dimensional Ising systems under the assumption that the interaction energies are random variables taking on continuous values and the distribution of the random variables is given by a continuous function. It is assumed that...

A numerical procedure of calculating the thermodynamic properties of the Ising models on the regular lattice is proposed. The procedure is explained for the regular Ising model on the square lattice, assuming the nearest-neighbour interaction.

A method of determining the ground state configurations of the Ising model by comparison of the energies of a small cluster of lattice sites is presented. The method is considered as the zero-temperature version of the cluster variation method. The method is illustrated by applying to the Ising...

The concept of thermodynamic limit in a stronger sense is introduced for random systems. It is then shown that the thermodynamic limit exists in the stronger sense for the one-dimensional random Ising model, under the assumption that the exchange integrals take values within a bounded interval....

The solution of the Fokker-Planck equation with spatial coordinate-dependent and time-dependent moments in many dimensions is given in the form of the path integral.

The free energy in the pair approximation of the cluster variation method is given in terms of the magnetizations of sites for the random Ising model. For a number of samples of the random-bond Ising model with nearest-neighbour interactions of +J and -J, on the square lattice, search is made of...