Critical Phenomena in Very Small Spin Systems

Abstract

AbstractThe discontinuities observable at second order phase transitions (e.g. the divergence of the specific heat) can occur only if the size of the considered system is very large (strictly speaking, infinite). Therefore some pronounced modifications of critical phenomena have to be expected in very small systems. We investigate these modifications by numerical calculations (using mainly the Monte Carlo method) for the case of both Ising S = 1/2 and classical Heisenberg spin systems (the total number of spins in the considered systems being in the range from 10 to 103). Assuming systems with free surfaces one finds also a pronounced dependence on the shape of the system. The shape dependence of the energy can be related to the reduction of the ground state energy of the system. Considering the behaviour of the energy, specific heat, and magnetization, one observes both a rounding of the critical anomalies and a shift to lower temperatures. This behaviour is in good agreement with the conclusions which can be drawn from the wellknown behaviour of the exactly soluble two‐dimensional Ising S = 1/2 model. The results for the three‐dimensional systems presented here give information concerning the rounding phenomena which should be observable at the “phase transition” of superparamagnetic grains or similar systems.