Critical behavior of the Blume-Emery-Griffiths model for a simple cubic lattice on the cellular automaton (Q2468257)

The Hamiltonian of the Blume-Emery-Griffiths (BEG) model is \[ H_I=-J\sum_{\langle ij \rangle}S_iS_j-K\sum_{\langle ij \rangle}S_i^2S_j^2-D\sum_iS_i^2, \] where \(S_i=\pm 1,0\) and \({\langle ij \rangle}\) denotes summation over all nearest-neighboring spin pairs on a simple cubic lattice. The parameters \(J\) and \(K\) are the bilinear and biquadratic interaction energies and \(D\) is the single-ion anisotropy constant. The authors study the three-dimensional BEG model using an improved heating algorithm from the Greutz cellular automation (microcanonical algorithm interpolating between the conventional Monte Carlo and molecular dynamics techniques on a cellular automaton), particularly, the re-entrant behaviour of the BEG model for the case \(-2\leq K/J\leq 0\), \(J>0\), \(0\leq D/J<3\), near the ferromagnetic phase and the stagger quadrupolar phase boundary and obtain the universality of the model in this region. For this purpose the temperature variations of the two-sublattice order parameters \(m_A\), \(m_B\) and \(q_A\), \(q_B\), the susceptibility \(\chi\) and the specific heat \(C\) are computed on a simple cubic lattice; the static critical exponents are estimated by analyzing the data within the framework of finite-size scaling theory. The obtained results are compatible with the universal Ising critical behaviour.