Abstract
Recently the finite lattice renormalization-group transformation (RGT) of Niemeijer and van Leeuwen1l (NvL) has proven very useful to evaluate critical exponents as well as critical temperatures for a two-dimensional Ising model. This method also has been applied to the system with higher lattice dimensionality2) ,sl and more complicated spin systems. 3) ~sl Although variational approximations for RGT2l yield the good results at d = 2, 3 and 4, in this letter we consider a slightly modified RGT with the same added proviso as in Ref. 4) for the prescription of the cell spins, which is simple and useful for the application to the more complicated spin systems at d=3. A direct application of NvL's method to a simple cubic lattice needs the odd-number spins, at least twentyseven spins, in each cubic cell. Therefore such calculations need many computational time. The present RGT is constructed according to the following procedures: A simple cubic lattice is divided into cells containing eight spins II (a= 1, · · ·, 8) and a extra spins 1I9 is put in the center of each cell for the prescription of the cell spin only, which does not interact with other spins and magnetic fields. A cell spin s' is associated ·with each cell for 28 ( = 256) configurations, with
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