Bidimensional Spin‐1/2 Ising Model in a Random Field

Abstract

The study of ferromagnetic systems in presence of random fields (RFIM) has received a great amount of interest in the last years.Pytte /l/ using a Gaussian distribution of random fields. They have found that the effect of increasing the width of distribution, h, is to decrease continuously the critical temperature until zero at a certain critical value, hc.Aharony /2/ has also treated the RFIM, with a symmetrical delta distribution, in the MF approximation and has obtained a tricritical behavior. ,A mean field treatment has also been done by Saxena /3/ in Heisenberg and transverse Ising models.In particular mean field (MF) calculations were performed by Schneider andThe differential operator method applied in Callen' s relation /4/ as introduced by Honmura and Kaneyoshi /5/ has been widely used in treating Ising Hamiltonians /6, 7/. The method provides better results than the MF approximation. Here we will use a delta distribution proposed by Grinstein and Mukamel/8/, which has as a particular case the distribution used in /2/ and /3/.The model is defined by the following Hamiltonian:where J sites g and p, 0 are Pauli matrices taking values +1,and H is the random g g field on the g-th site. is the constant exchange interaction between two nearest neighbouring gP -Callen' s identity for spin -1/2 is given by /4, 6/ ( .,{g>)= ({g) tanh(BEg)) 9 -1 ) Caixa Postal 702,

Ising Model with Random Local Fields in a Two‐Dimensional Ferromagnet

“…A similar distribution function as that proposed in [5] was discussed in detail by Borges and Silva [6] for the cases of planar square and triangle lattices and then also for the simple cubic lattice. In this paper Callen's identity was considered with the use of the differential operator method, proposed by Honmura and Kaneyoshi [ 7 ] .…”

“…where and A4(l), A4(3) are the same coefficients as those derived in [6]. It can be noted here that our equations (11) and (12) are given in the same form as corresponding equations derived by Matsudaira for a perfect crystal and diluted alloy cases, with only different coefficients X and Y .…”

“…3 of the cited paper. However, we have made also calculations for other values of p which revealed some properties of the phase diagrams overlooked in [6].…”

“…As a result the phase diagrams and magnetization curves were obtained. I n particular it appeared that for the planar lattices the phase diagrams obtained in [6] correspond to the second-order phase transition. No tricritical point and first-order phase transition were obtained there.…”

The diluted mixed spin‐1/2 and spin‐3/2 Ising model in a longitudinal random field

“…In particular, the bimodal distribution yields a tricritical point, while for a model with a Gaussian distribution of random fields the phase transition remains of second-order. Afterwards, the existence of a tricritical behavior has been examined by the use of various techniques, such as meanfield theory [15], Monte Carlo simulations [16,17], renormalization-group calculations [18], Bethe-Peieris approximation [19] and effective-field theory [20][21][22] …”