Role of nearest‐neighbour correlations in the site‐diluted spin‐1/2 Ising model

Abstract

For many years now there has been extensive study of the second-order phase transition in the diluted Ising model. The points of interest in the theoretical and the experimental studies of such disordered magnets are the concentration dependence of the critical temperature and the value of the critical concentration of magnetic atoms below which the system will not exhibit a transition to magnetic order. Due to the fact that for both two-and three-dimensional systems no exact solution is known for the model, the presently available results are all based on theoretical approximations or computer simulations.In particular, among the successful methods used to tackle the problem, there have been the one-[ l , 21 and two-spin [3] cluster approximations. However, the results of [3] are based on the decoupling approximation that neglects the correlations not only between nextnearest neighbours but also between nearest neighbours. Therefore, further improvement to the theory will result if at least nearest-neighbour correlations are taken into account. This has been illustrated in the present note for the square lattice.The Hamiltonian of our system is given by where (i, j ) runs over all nearest-neighbour pairs of spins, ti = l(0) if the site i is occupied (unoccupied) by a magnetic atom and J is the exchange interaction.According to [3], we can obtain an exact equation for a pair of neighbouring spins as follows: (( t j ( 1 -ti) k ' = ' fi' 1 Bk'))c tanh T I x=o,y=o ') Moyzesova 16, 041 54 Koiice, Slovakia.