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   <subfield code="a">The ( k B T C/ zJ , k ) Phase Diagram for the D</subfield>
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   <subfield code="a">The 4-d spin-1 Ising (BEG) model has been simulated using a cellular automaton (CA) cooling algorithm improved from the 3-d BEG model algorithm for the four-dimensional hypercubic lattices. The ground state diagram (k,d) of the 4-d BEG model has ferromagnetic (F), quadruple (Q) and staggered quadruple (SQ) ordering regions. The simulations have been made in the −3≤k=K/J≤1 interval through the d=1 line for L=18 lattice size. The (k B T C/zJ,k) phase diagram has been obtained through the d=1 phase line. The results show that the model has a bicritical point (BCP) as in d&lt;4 dimensions. The phase diagram has been separated to the three regions of the staggered quadruple (SQ), the ferromagnetic (F) and the paramagnetic (P) cases.</subfield>
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