Curie temperature T C of spin arrangement with arbitrary dimension was considered. We assumed that interaction of a spin with all other spins vary with a power-law decay rate in exchange integral on Heisenberg model. As a result, we found that T C , which was obtained from T C = λC (λ: mean-field coefficient and C: Curie constant), significantly depends on fractal dimension of spin arrangements D, the exchange integral and the decay constant. This semi-quantitavely explains how T C depends on D (1 ≤ D ≤ 3) in a universal way and also the finite size effect on T C in low-dimensional spin systems.

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