Critical behaviour of a compressible n-component model with cubic anisotropy

Abstract

A generalisation of a model, in which an n-component order parameter Phi is coupled to an elastic continuum, to the case of cubic anisotropy is studied in a renormalisation group calculation. It is shown to all orders in epsilon =4-d that the inclusion of cubic anisotropy in the coupling terms yields a second-order transition if and only if all alpha _i=2_{phi i}-vd0 (e.g. Ising and anisotropic XY and Heisenberg model) the absence of a stable fixed point is interpreted as a first-order transition. If the transition is close to second-order, renormalised exponents may be observed. The generalisation of the results to the case of lower symmetry and their relevance for other systems with non-analytic interaction is mentioned.