Crossover in the Heisenberg ferromagnet

By comparing the free energies of the random phase approximation and of the exact expansion to order 1/z², the authors find a crossover between a low-temperature spin-wave regime and a high-temperature nonlinear regime in the magnetic state of a Heisenberg ferromagnet. Above the crossover, the many-body interactions between the spin fluctuations become important and the kinematic constraints must be maintained. This crossover is revealed by a quantum peak in the fluctuation specific heat. Experiments have observed a peak in the specific heat C/T very close to the predicted crossover temperature.