On the decay of anisotropy approaching the critical point

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Abstract
A recent investigation by Nattermann and Trimper, (see J. Phys. A., vol.8, p.200, 1975), of the influence of cubic anisotropy in both the quadratic and quartic parts of an n-component order parameter Hamiltonian is extended in order to examine the decay of the anisotropy near the critical point. In the case where the transition is driven to first order by the anisotropic fluctuations, the 'size' of the first-order transition is estimated. It turns out that this first-order transition becomes experimentally observable only for large values of the lattice anisotropy. The effective and asymptotic critical exponents eta and zeta (the latter characterizes the decay of the anisotropy) are calculated. The competition between the decay of the anisotropy and the occurrence of a first-order transition in investigated. The results give an explanation for the first-order transition in KMnF3. The extension of this approach to lower-than-cubic symmetry is briefly discussed.