Large-n critical behavior of O(n)×O(m) spin models Original Research Article

We consider the Landau–Ginzburg–Wilson Hamiltonian with O(n)×O(m) symmetry and compute the critical exponents at all fixed points to O(n−2) and to O(ϵ3) in a ϵ=4−d expansion. We also consider the corresponding non-linear σ-model and determine the fixed points and the critical exponents to O(ϵ̃2) in the ϵ̃=d−2 expansion. Using these results, we draw quite general conclusions on the fixed-point structure of models with O(n)×O(m) symmetry for n large and all 2⩽d⩽4.