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Chinese Physics Letters

Finite-Size Scaling Analysis of a Three-Dimensional Blume–Capel Model in the Presence of External Magnetic Field

H Demirel, A. ÖZKAN, Bülent Kutlu

Published Jul 1, 2008• 1 citation
Publisher

Abstract

The Blume–Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent δ is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range −0.1 ≤ h = H/J ≤ 0. The estimated value of the field critical exponent δ is in good agreement with the universal value (δ = 5) in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.

DOI
10.1088/0256-307x/25/7/073

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The Blume–Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent δ is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range −0.1 ≤ h = H/J ≤ 0. The estimated value of the field critical exponent δ is in good agreement with the universal value (δ = 5) in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.
The four-dimensional ferromagnetic Ising model in external magnetic field is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice, Tcχ(∞)=6,680(1) obtained for h = 0 agrees well with the values Tc(∞)≈ 6.68 obtained previously using different methods. Moreover, h = 0.00025 in our work also agrees with all the results obtained from h = 0 in the literature. However, there are no works for h ≠ 0 in the literature. The value of the field critical exponent (δ = 3.0136(3)) is in good agreement with δ = 3 which is obtained from scaling law of Widom. In spite of the finite-size scaling relations of |ML(t)| and χL(t) for 0 ≤ h ≤ 0.001 are verified; however, in the cases of 0.0025 ≤ h ≤ 0.1 they are not verified.
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain z=2.0245(15) for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our estimate of z is fully consistent with recent field theoretic results.
The five-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4≤L≤16. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.52(7) and 1.25(11) using 6≤L≤12, respectively, which are in very good agreement with the Monte Carlo results and with the theoretical predictions of 5/2 and 5/4. The critical temperature for the infinite lattice is found to be 8.779(8) using 8≤L≤16 which is also in very good agreement with the recent precise results.
The spin-3/2 Blume—Capel model is studied using the heating and cooling algorithms improved from the Creutz cellular automaton (CCA). The calculations are done on various sizes of the simple cubic lattice in the 0 ≤ D / J ≤ 5 parameter region. The phase diagram of the model and temperature variation of the thermodynamic quantities are obtained. We confirm the existence of a critical end point within the heating calculations. However, in contrast to the heating calculations, we do not obtain the first-order line at low temperature with cooling algorithm calculations. The results are compared with those of other theories.