Monte Carlo Studies of Tricritical Phenomena

Thermodynamically self-consistent theory for the Blume-Capel model

“…Similarly, for the fcc lattice, we find k B T t /J = 3.1116 ± 0.0090, τ t = 0.2454 ± 0.0010 (∆ t /J = 5.6520), x t = 0.658 ± 0.006, which we may compare with the MonteCarlo estimates of Jain and Landau [13] k B T t /J = 3.072 ± 0.024, ∆ t /J = 5.652 ± 0.048, x t = 0.56 ± 0.02 (note that our value of x t is in much better agreement with the series expansion estimate of Saul et al [11], x t = 0.665…”

“…Mean-field theory [8] predicts that the critical field h c should go to infinity at k B T c /Jc = Monte-Carlo simulations of Jain and Landau [13].…”

“…This model has played an important role in the development of the theory of tricritical phenomena [9,10] and has been very actively studied over the years, following the original mean field treatment of BEG [8]. Various methods like series expansions [11], renormalization-group calculations [12], and Monte-Carlo simulations [13] have been used to describe the first-and second order regions, the tricritical region, and the crossover between them. A study of the coexistence curve using the mean-spherical approximation has also been proposed recently [14].…”

Hysteresis and compensation behaviors of spin-3/2 cylindrical Ising nanotube system

“…BC model has been studied with many different techniques, such as mean field approximation (MFA) [10], effective field theory (EFT) [11][12][13], Bethe approximation [14], Monte Carlo simulation (MCs) [15], renormalization group theory [16] and the cluster variational approximation [17,18], and it was found that it exhibits very interesting and rich critical phenomena.…”

Anomalies in the multicritical behavior of staggered magnetic and direct magnetic susceptibilities of iron group dihalides

“…Some theoretical Hamiltonian models describing the behavior of iron group dihalides have been proposed. Monte-Carlo simulation [36,37] and high-temperature series expansion calculations [38,39] have been performed on a simple cubic lattice Ising model with in-plane ferromagnetic coupling and antiferromagnetic coupling between adjacent planes (the meta model) and on the next-nearest-neighbor (nnn) model with antiferromagnetic nearest-neighbor (nn) and ferromagnetic next nearest-neighbor (nnn) interactions. Recently, a MC simulation has been performed on a quite realistic model of F eCl 2 in a magnetic field [44] and this typical metamagnet has also been treated by a high-density expansion method on a two-sublattice collinear Heisenberg Ising (s = 1) model with three-and four-ion anisotropy [45,46].…”