Abstract
A real space renormalization group approach with two-terminal clusters is proposed for the calculation of the specific heat and spontaneous magnetization (for all temperatures) of the nearest-neighbour spin −1/2 Ising ferromagnet in simple cubic and hypercubic lattices. For arbitrary temperatures only small clusters (renormalization expansion factorb=2,3 ford=3 andb=2 ford=4) are considered: they lead to reasonable values for the critical points, exponents and amplitudes, to a thermal behaviour of the spontaneous magnetization which is already quite close to what is expected (from series results for example) but to a thermal behaviour of the specific heat which is not yet very close to what is expected. The global results improve whenb increases from 2 to 3. The drastic effect (on the specific heat) of an apparently innocuous approximation is exhibited. The discussion of theT→0 andT→∞ limits is performed and theexact behaviours of the free and internal energies and the specific heat are obtained for sufficiently large values ofb andall dimensionalities.
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