An introduced effective-field approximation and Monte Carlo study of a spin-1 Blume–Capel model on a square lattice

Abstract

The magnetic properties of a spin-1 Blume-Capel (BC) model on a square lattice (q = 4) with a ferromagnetic interaction have been examined here by the use of Monte Carlo (MC) simulation technique and an introduced effective-field approximation (IEFT), which includes the correlations between different spins that emerge when expanding the identities. The effects of the external magnetic field and crystal field on the magnetic properties of the spin system are discussed in detail. In order to obtain credible results, a detailed comparison of the results obtained by the two methods has been made with those of the other methods in the literature. A number of interesting phenomena originating from the temperature, crystal field and external field have been found.

Correlation identities and rigorous upper bounds on the critical temperature for the spin-1 Blume–Capel model on a Kagome lattice

“…We can see that the results of the mean field approximation and effective field approximation for the Blume-Capel model on a Kagome lattice present a behavior similar to the hexagonal and the square lattice, obtained by other works [7][8][9]14,18].…”

“…The spin-1 Blume-Capel model was studied by a variety of methods such as mean-field approximation (MFA) [1,2], effective-field approximation (EFA) [4][5][6][7][8][9], the Bethe lattice approximation [10], series expansion method (SE) [11,12], cluster variation method (CVM) [13], Monte Carlo (MC) simulations [14][15][16][17], renormalization-group (RG) method [18,19] and rigorous inequality correlation function [20][21][22]. Most of these studies were done on hexagonal and rectangular lattices.…”

The Blume–Capel model for spins S=1 and 3∕2 in dimensions Butera1, Pernici2 2018Physica A: Statistical Mechanics and its Applications343360View full textAdd to dashboardCite

“…Many MC simulations of accuracy increasing with the speed and memory of the available computers, were carried out on the sq 20,24,29,38,39 , on the sc 30,32,33 , and the f cc lattices 25 for the BC model with various values of the spin. In particular a very recent multicanonical simulation 39 for the sq lattice reaches a very high accuracy.…”

“…The BC model has been explored in a variety of analytical approximations (mean field (MF), effective field, Renormalization Group, etc.) 1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] , by transfer-matrix methods [21][22][23] and by MonteCarlo (MC) simulation methods 14,20,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] , but only in a handful of papers [40][41][42][43][44][45] extrapolations of series-expansions were employed, in spite of the potential reliability and accuracy of this technique. The high-temperature (HT) and the low-temperature (LT) expansions have been jointly used 43 to map out the phase diagram, (the former being generally sufficient to locate the second-order part of the phase-boundary and to determine its universal parameters, the l...…”

Static quadrupolar susceptibility for a Blume–Emery–Griffiths model based on the mean-field approximation

“…Also, several investigations concentrated on the dipolar (or magnetic) susceptibility (χ m ) which is defined by the response of dipolar order parameter (or magnetization) to the external magnetic field. The temperature and magnetic field variations of χ m for spin-1 BEG model were studied and its splitting into two branches was discussed by various authors [24][25][26].…”