The critical behavior of four dimentional Spin-1 Ising (Blume-Capel) model

In this thesis, the 4-dimensional Blume-Capel(BC) model is simulated using the cooling and the heating algorithms which improved from the Creutz Cellular Automaton for hypercube lattice. The values of the critical temperatures(kTc/J) and the static critical exponents(?, ß, ? and ?) are estimated within the framework of the finite size scaling theory for d 4. The simulations shown that the model has a tricritical point at the D/J=3.7 single-ion anisotropy parameter value. In this point, the static critical exponents are estimated as ?=0.03, ?=1.16, ß=0.58 and ?=0.58 values. These values are different from universal values(?=0, ß=1/2, ?=1 and ?=1/2). In the other hand, for D/J=3 value in the D/J<3.7 parameter reqion the estimated statical critical exponents are in good agreement with universal values. This case indicated that the BC model exhibits an ununiversal critical behavour near the tricritical point. The simulations were carried out on the finite hypercube lattices with periodic boundary conditions.