Monte Carlo Calculations on a Lattice with Random Spin Interactions

A Monte Carlo procedure is introduced in which spin-flip dynamics are applied to a system that is characterized through random radial dependence of the exchange interaction. Application is made to a dilute system such as P in Si, where a topological distribution of spin orientation affects the measured magnetic susceptibility. Although a transition temperature is not clearly defined, a Curie-Weiss description is possible, the nature of which can still characterize the concentration of spins in the material. The spin dynamics does not directly reveal evidence of spin clustering and is not a valid approach below the transition temperature where quantum molecular effects dominate.