Classical and quantum quasi-1D Heisenberg model with competing interactions

In this paper the authors examine the zero-temperature phase diagram and ground-state configurations of a Heisenberg Hamiltonian with exchange competition up to third-nearest neighbour in 1D (linear chain). In the classical limit S to infinity they find that the ground state is ferromagnetic, antiferromagnetic or modulated depending on the interactions. Transitions between the various phases are all first order with the exception of a finite portion of the boundary between the ferromagnetic and the helical phases, where the transition is continuous. The authors also study the quantum model by means of a perturbative approach that evaluates the zero-point-motion energy to order 1/S in the non-collinear phases, thus establishing the relative location of the quantum ground-state configurations. However, one can evaluate to all orders in 1/S the exact expression of the zero-point motion for vanishing helix wavevectors in the vicinity of the second-order ferro-helix classical transition line. The result is that a finite part of the ferro-helix classical line is swept away by quantum fluctuations and replaced by a first-order transition. The scenario should be realistic at low but finite temperature, and should indicate the relevance of quantum effects even on the critical behaviour in quasi-1D systems with very-low-temperature transitions.