Low-temperature renormalization-group study of the random-axis model

Abstract

Momentum-shell recursion relations valid for low temperatures and small anisotropy are generated for the random-axis model of amorphous magnetism. The fixed-point structure of these relations suggests that ferromagnetism is absent below four dimensions. The critical behavior along the ferromagnetic—spin-glass phase boundary above four dimensions is explored, and, at least to first order in $\epsilon =d-4\mathrm{}$, the exponents, hyperscaling law, and behavior of the longitudinal susceptibility are identical to a nonrandom model in two dimensions less. We also present an attempt at a Mermin-Wagner proof of the absence of ferromagnetism below four dimensions, utilizing the replica method.