Critical Exponents of the 3-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}$D/J=2.82${\small value are estimated for the standard and the cooling algorithms which improved from Creutz Cellular Automaton. The analysis of the data using the finite-size scaling and power law relations reproduce their well-established values in the}$D/J<3${\small and }$D/J<2.8${\small parameter region at standard and cooling algorithm, respectively. For the cooling algorithm at}$D/J=2.8$% {\small value of single-ion anisotropy parameter, the static critical exponents are estimated as}$\beta =0.31${\small ,}$\gamma =\gamma ^{\prime}=1.6${\small ,}$\alpha =\alpha ^{\prime}=0.32${\small and}$\nu =0.87$% {\small . These values are different from}$\beta =0.31${\small ,}$\gamma =\gamma ^{\prime}=1.25${\small ,}$\alpha =\alpha ^{\prime}=0.12${\small and}$\nu =0.64${\small universal values. This case indicated that the BC model exhibit an ununiversal critical behavior at the}$D/J=2.8${\small parameter value near the tricrital point(}$D/J=2.82${\small). The simulations carried out on a simple cubic lattice with periodic boundary conditions.