Relaxation phenomena in two interacting spin lattices

The authors study the kinetics of the formation of antiferromagnetic order in a finite spin system. The system is initially forced to be an unstable ferromagnetic state by means of an external field. When the field is switched off the system decays toward equilibrium. The finite size of the system has relevant consequences on the time of persistence of the initial unstable state. The fluctuations driving the system to equilibrium become anomalously large in the transient. The authors obtain analytic results for the transient fluctuation statistics in the limit where the average squared magnetisation relaxes much more quickly than relative orientation of the sublattices. The results have been obtained in the framework of spherical model and of molecular field approximation. The relaxation dynamics are ruled by the nonlinear Langevin equations