Critical exponents of the three-dimensional Blume–Capel model on a cellular automaton

Abstract

The static critical exponents of the three dimensional Blume-Capel model

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

“…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...…”

Re-entrant phase transitions of the Blume–Emery–Griffiths model for a simple cubic lattice on the cellular automaton

“…The parameters of J and K are the bilinear and biquadratic interaction energies, respectively and D is the single-ion anisotropy constant. The three-dimensional BEG model has been extensively studied by different techniques, using the mean-field approximation (MFA) (1,5−7) , effective-field theory (8−11) , two-particle cluster approximation (TPCA) 12 , Bethe approximation 13 , high-temperature series expansion 14 , renormalization group theory 15 , Monte Carlo simulations (13,16−17) , linear chain approximation (18,19) and cellular automaton (20,21) In this paper we studied the three-dimensional BEG model using an improved heating algorithm from the Creutz Cellular Automaton (CCA) for simple cubic lattice. The CCA algorithm is a microcanonical algorithm interpolating between the canonical Monte Carlo and molecular dynamics techniques on a cellular automaton, and it was first introduced by Creutz 22 .…”

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

“…Furthermore, the results obtained using CA algorithm and its improved versions are in good agreement with the universal critical behavior for the BEG model. Thus the simulations have been carried out using a cellular automaton heating algorithm which successfully produces the critical behavior of the Ising model [12,[32][33][34].…”

“…The finite lattice critical temperatures are estimated from the maxima of the susceptibility (χ) for the fcc lattice with periodic boundary conditions. In order to expose the influence of the dipole-quadrupole interaction, the thermodynamic quantities have been calculated using CA heating [12,[32][33][34] algorithm on the fcc lattice for L = 4 6 8 9 and 12 (The total number of sites is N = 4L 3 ) with the periodic boundary conditions. The fcc lattice can be built from four interpenetrating simple cubic lattices.…”