The Critical Behavior of the General Spin Blume–Capel Model

Abstract

The general spin-S Blume-Capel model is studied within two different approaches: the pair approximation for the free energy, and Monte Carlo simulations. The global phase diagram in the temperature-anisotropy plane is obtained for general values of S in the pair approximation and the results are qualitatively the same as those of the usual mean field theory. Special interest is given in the low temperature region of the phase diagram where a number of first-order lines emerge from a multiphase point at the ground state. Monte Carlo simulations for S = 1, 3/2, and 2 on simple cubic lattices also confirm the general trend of the mean field like approach, and in the special S = 3/2 case the present results are in disagreement with previous Monte Carlo simulations, as well as renormalization group calculations on corresponding two-dimensional lattices.PACS number(s): 05.70.F, 64.60.A, 75.10H

The Blume–Capel model for spins S=1 and 3∕2 in dimensions Butera1, Pernici2 2018Physica A: Statistical Mechanics and its Applications333360View full textAdd to dashboardCite

“…In conclusion, also in 3d the behavior of the spin S = 3/2 model appears qualitatively different from that of the spin S = 1 model. As D varies, the exponent estimates remain Ising-like and thus consistent with the expected universality properties and with a previous MC simulation 13 confirming the absence of a TCP followed by a first-order line. The validity of the structural prediction of the MF approximation, at least for the model with the lowest non-trivial half-odd spin value is thereby confirmed.…”

“…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...…”

Quantum Model for Ferromagnetic Thin Films with an Alternating Crystal Field

“…The ferromagnetic Blume-Capel-Ising (BCI) model has been studied within the mean field approximation [1], the effective field theory [2], the two-spin cluster approximation in the cluster expansion method [3,4], Monte Carlo simulations [5], a thermodynamically self-consistent theory based on an Ornstein-Zernike approximation [6], the exact solution based on the Bethe lattice by means of the exact recursion relations [7]. Most of the studies mentioned above displays also the existence of a tricritical point at which the phase transition changes from second order to first order when the value of K 2 becomes negative.…”

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

“…The case where S = 1 has been extensively studied by several approximate techniques in two-and three-dimensions and its phase diagram is well established [29][30][31][32][33][34][35]. The case S > 1 has also been investigated according to several procedures [36][37][38][39][40][41][42]. The simulations have been performed for ∆ = 0, which is the simplest case, on different lattice sizes comprising a number N = 1000, 2000, 4000, 8000, 16000 and 32000 of sites.…”