Fizika Nizkikh Temperatur: Volume 48, Number 6 (June 2022), p. 542-551    ( to contents , go back )

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

pos Анотація:1184

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.

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