Thermodynamics and dynamics of spin systems in the phase transition to the superradiant state

Phase transition to the superradiance (spontaneous coherent) state in the system of classical spins interacting with resonance field is investigated. Thermodynamic properties of the system are determined by means of the exact calculation of the partition function. It is shown that the coherent state of the spins arisses below the transition point. Dynamical susceptibility of the system near to and far from the transition point is found in the case of the uniform field by means of averaging the exact solution of the equations of motion. It is shown that in the region far from the transition point the width of the spectrum is getting anomalously large and is determined, on the whole, by the constant of coupling of spins with the field.