Critical behavior of compressible magnets

Abstract

A model of a compressible $n$-component magnet which includes shearing forces is solved by the renormalization-group recursion relations to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$. Four fixed points are found and their relevance for critical behavior is discussed. The critical exponents of Heisenberg magnets have their rigid-lattice values. The leading correction to scaling has the exponent $\ensuremath{\alpha}{\ensuremath{\nu}}^{\ensuremath{-}1}$ with respect to inverse length. In Ising-like systems the transition is of the first order, but may appear as a second order.