Correlation between Curie temperature and system dimension

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