Quantum fluctuations and phase diagram of Heisenberg models with competing interactions

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Abstract
The T=0K phase diagram of the Heisenberg model for finite S on the square lattice with exchange interaction up to third neighbours is studied. The nearest-neighbour interaction is assumed to be ferromagnetic. In the classical (S to infinity ) approximation the model has, in addition to the ferromagnetic phase, an antiferromagnetic and two non-equivalent helical phases depending on the amount of competition between the interactions. To lowest order in 1/S these phases are still present but quantum fluctuations bring a significant modification to the phase diagram: with the exception of the ferro-helix transition line, all the phase boundaries are shifted with a considerable enhancement of the region with antiferromagnetic order. In addition, between the two non-equivalent helices a new phase sets in which is characterised by an infinite degeneracy of the ground state with absence of long-range order even at T=0K. In the S to infinity limit this phase collapses into line in the parameter space.

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