Correlation between Curie temperature and system dimension

Curie temperature TCTC 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 TCTC, which was obtained from TC=λCTC=λC (λλ: 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-quantitatively explains how TCTC depends on D   (1≤D≤31≤D≤3) in a universal way and also the finite size effect on TCTC in low-dimensional spin systems.