Renormalisation-group approach to the magnetic phase transition in solid3He

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Abstract
A renormalisation-group approach is proposed to account for the qualitative features of the magnetic phase transition in solid 3He. The study suggests that the first-order transition at 1.1 mK may be associated with a transition from a paramagnetic to a type-II antiferromagnetic phase. The n=6-component Landau-Ginzburg-Wilson Hamiltonian corresponding to this transition is constructed. The model is found to exhibit no stable fixed point in d=4- epsilon dimensions, indicating a first-order transition. The relation of this model to microscopic models such as the Heisenberg model with nearest- and next-nearest-neighbour interactions and models with four-spin interaction is discussed. The effect of symmetry-breaking magnetic fields on the order of the transition is also considered.