Critical behavior of a 3-D Ising model in a random field

Abstract

A Monte Carlo method has been used to study a simple cubic Ising ferromagnet in a random quenched magnetic field. The Hamiltonian for this model is ℋ==JΣ(ij)σiσj−ΣiHiσi, where σi,σj=±1, J is the nearest-neighbor interaction constant, and the field Hi=tH is fixed at each site with ti=±1 at random and Σti=0. L×L×L lattices with periodic boundary conditions have been studied for a range of H and T. As expected we find a ferromagnetic ordered state which for small H undergoes a second order phase change to the paramagnetic state with increasing temperature. A finite size scaling analysis of the preliminary data suggests that the critical exponent β is substantially smaller (β∼0.2) than the usual 3-dim Ising value of 0.31. Results obtained for small lattices indicate that below kT/J-2 the transition becomes first order suggesting that a tricritical point appears on the critcal field curve.

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

“…On the other hand, Aharony [18] showed within the framework of the same approximation that a tricritical point be observed for a model with a two-peak d-distribution function. Theoretically, the RFIM has been widely investigated by the use of various techniques, including the mean-field-approximation calculations [19][20][21], renormalization calculations [22][23][24][25][26] and Monte Carlo simulation [27][28][29], Bethe-Peierls approximation [30] and effectivefield theories (EFT) [31][32][33]. It is worth noting that the analyses of the RFIM have been almost restricted to the simple spin-1/2 systems.…”

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] …”

Trimodal random‐field distribution of a mixed spin Ising model

“…In particular, a bimodal distribution yields a tricritical point, while for a model with a Gaussian distribution of random fields the phase transition remains of second order. The existence of tricritical behavior has been examined using various techniques, such as mean field theory [15], Monte Carlo simulations [16,17], renormalization group calculations [18], the Bethe-Peieris approximation [19], and effective field theory (EFT) [20 -22]. It is worth noting that the analyses of the RFIM have been mostly restricted to simple spin-1/2 systems.…”