Correlation between Curie temperature and system dimension

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 = lambda C (lambda: 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 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. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.