Bi- and tetracritical phase diagrams in three dimensions

Abstract

The critical behavior of many physical systems involves two competing $n_1^{}-$ and $n_2^{}-$component order-parameters, ${\mathbf{S}}_1^{}$ and ${\mathbf{S}}_2^{}$, respectively, with $n=n_1^{}+n_2^{}$. Varying an external control parameter $g$, %(e.g. uniaxial stress or magnetic field), one encounters ordering of ${\mathbf{S}}_1^{}$ below a critical (second-order) line for $g<0$ and of ${\mathbf{S}}_2^{}$ below another critical line for $g>0$. 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.

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Cited by in corpus (2)

• Anomalous Dimensions in Hypercubic Theories
• ${\varphi }^4$ lattice model with cubic symmetry in three dimensions: RG-flow and first order phase transitions