Bi- and tetracritical phase diagrams in three dimensions
Amnon Aharony, Ora Entin-Wohlman, and Andrey Kudlis
School of physics and astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
Received March 1, 2022, published online April 25, 2022
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.