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 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.