Abstract

The critical behavior of many physical systems involves two competing n₁- and n₂-component order-parameters, S₁ and S₂, respectively, with n=n₁+n₂. Varying an external control parameter g, one encounters ordering of S₁ below a critical (second-order) line for 0 < g and of S₂ below another critical line for 0 > g. These two ordered phases are separated by a first-order line, which meets the above critical lines at a bicritical point, or by an intermediate (mixed) phase, bounded by two critical lines, which meet the above critical lines at a tetracritical point. For n=1+2=3, the critical behavior around the (bi- or tetra-) multicritical point either belongs to the universality class of a non-rotationally invariant (cubic or biconical) fixed point, or it has a fluctuation driven first-order transition. These asymptotic behaviors arise only very close to the transitions. We present accurate renormalization-group flow trajectories yielding the effective crossover exponents near multicriticality.

Key words: renormalization-group, phase diagrams, bicritical point, tetracritical point.