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

The static critical exponents of the three-dimensional Blume–Capel model which has a tricritical point at D/J=2.82 value are estimated for the standard and the cooling algorithms which improved from Creutz cellular automaton. The analyses of the data using the finite-size scaling and power-law relations reproduce their well-established values in the D/J<3 and D/J<2.8 parameter region at standard and cooling algorithms, respectively. For the cooling algorithm at D/J=2.8 value of single-ion anisotropy parameter, the static critical exponents are estimated as β=0.31, γ=γ′=1.6, α=α′=0.32 and ν=0.87. These values are different from β=0.31, γ=γ′=1.25, α=α′=0.12 and ν=0.64 universal values. This case indicated that the BC model exhibits an ununiversal critical behavior at the D/J=2.8 parameter value near the tricritical point (D/J=2.82). The simulations were carried out on a simple cubic lattice with periodic boundary conditions.