Abstract
We use mean-field and renormalization-group techniques to study the phase diagram of a spin-1 Ising ferromagnet in a random crystal field. The mean-field equations, which can be obtained either with or without using the replica trick, yield a rich phase diagram, with some new transition lines and multicritical points, for both a bimodal delta-function and a Gaussian distribution of anisotropics. The replica trick is then used to write an effective n-component hamiltonian in momentum space. To leading order in e, recursion relations in 4-e dimensions yield a stable and symmetric fixed point which cannot be reached from physical initial conditions. Within a replica-symmetric picture, however, it is possible to reconcile the mean-field and the e-expansion calculations.
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