A SELF-CONSISTENT THEORY OF PHASE-TRANSITIONS IN NONCOLLINEAR MAGNETS

I study phase transitions occurring in noncollinear magnets by means o f a self-consistent screening approximation. The Ginzburg-Landau theor y involves two N-component vector fields with two independent quartic couplings allowing a symmetry-breaking scheme which is SO(N) x SO(2) - -> SO(N - 2) x SO(2)(diag). I find that there is a second-order phase transition in the physical cases N = 2, 3, D = 3 and that there is no fluctuation-induced first-order transition. This is very similar to th e case of the normal-to-superconducting phase transition as recently f ound by Radzihovsky. The exponents are (eta)(N= 3; D = 3) approximate to 0.11, (eta)(N = 2, D = 3) approximate to 0.15 and go smoothly to th e large-N limit.