Abstract
Recent applications of the renormalization group to critical phenomena in magnetic systems have been based mainly on local linear arguments. It has been implicitly assumed that the global nonlinear effects are important only in crossover effects and that the behavior asymptotically close to the critical point is determined by the stablest fixed point alone. We have given a nonlinear analysis which incorporates the crossover between the Wilson–Fisher and mean field behavior. We point out in this paper that this competition expresses itself in globally valid solutions which can upset the dominance presumed from the linear stability analysis unless certain regularity conditions are imposed.
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