Abstract
We use renormalization-group techniques to investigate a model of O(n)/O(n-m) symmetry breaking in 4-\ensuremath{\varepsilon} dimensions. The model describes n-component spin systems in which varying levels of frustration indexed by m\ensuremath{\le}n give rise to canted ground states. The order parameter for these magnets is a reference frame with m orthogonal axes. The model contains the triangular antiferromagnet as a special case. We compute fixed points and critical exponents to scrO(\ensuremath{\varepsilon}) from the renormalization-group recursion relations. We find that a second-order phase transition with O(n)/O(n-m) symmetry breaking occurs for restricted values of m and n. Higher levels of frustration are shown to drive the transition to first order. Finally, we explore a closely related model of U(n)/U(n-m) symmetry breaking, wherein similar results are found.
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