Critical behavior of compressible magnets

A model of a compressible $n$-component magnet which includes shearing forces is solved by the renormalization-group recursion relations to first order in $\epsilon =4-d$. 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 $\alpha {\nu }^{-1\mathrm{}}$ with respect to inverse length. In Ising-like systems the transition is of the first order, but may appear as a second order.