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Physica A Statistical Mechanics and its Applications

New effective-field theory for the Blume-Capel model

Aline Franco Siqueira, I. P. Fittipaldi

Published Oct 1, 1986• 79 citations
Publisher
DOI
10.1016/0378-4371(86)90035-x

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Effective-field and Monte Carlo studies of a kinetic Blume–Capel model

Xiaoling Shi, Guozhu Wei

It has been well established that the spin-1 Blume–Capel (BC) model in a time-dependent oscillating external field and a crystal field interaction exhibits a rich variety of topology in nonequilibrium dynamic phase diagrams. Some interesting dynamic behaviors, quite different from the standard Ising model, have been observed. However, there are some disagreements among these theoretical studies. Here we use the effective-field theory (EFT) and the Monte Carlo method (MC) to show that the dissimilarity among the mean-field theory and EFT results is due to the neglect of thermal fluctuations. The effects of thermal fluctuations on the dynamic phase boundary and the dynamic tricritical point are investigated. The MC method is then carried out to confirm if the reentrant phenomenon obtained by the EFT is correct or not. The dynamic phase diagram of the kinetic BC model given by the MC method is also plotted.

Physica Scripta•Jun 6, 2014•10 citations
A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume–Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.
It has been well established that the spin-1 Blume–Capel (BC) model in a time-dependent oscillating external field and a crystal field interaction exhibits a rich variety of topology in nonequilibrium dynamic phase diagrams. Some interesting dynamic behaviors, quite different from the standard Ising model, have been observed. However, there are some disagreements among these theoretical studies. Here we use the effective-field theory (EFT) and the Monte Carlo method (MC) to show that the dissimilarity among the mean-field theory and EFT results is due to the neglect of thermal fluctuations. The effects of thermal fluctuations on the dynamic phase boundary and the dynamic tricritical point are investigated. The MC method is then carried out to confirm if the reentrant phenomenon obtained by the EFT is correct or not. The dynamic phase diagram of the kinetic BC model given by the MC method is also plotted.