Abstract
The field-theoretical model describing multicritical phenomena with two coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||}) \oplus O(n_{\perp}) symmetry is considered. Conditions for realization of different types of multicritical behaviour are studied within the field-theoretical renormalization group approach. Surfaces separating stability regions for certain types of multicritical behaviour in parametric space of order parameter dimensions and space dimension d are calculated using the two-loop renormalization group functions. Series for the order parameter marginal dimensions that control the crossover between different universality classes are extracted up to the fourth order in \varepsilon=4-d and to the fifth order in a pseudo-\varepsilon parameter using the known high-order perturbative expansions for isotropic and cubic models. Special attention is paid to a particular case of O(1) \oplus O(2) symmetric model relevant for description of anisotropic antiferromagnets in an external magnetic field.
Highlights
The concept of universality plays a paradigmatic role in the modern statistical physics
In the n–d-space, the regions of stable fixed point (FP) are separated by borders and the n(d) curves define the order parameter (OP) marginal dimensions that control the crossover between different universality classes
In the present paper we have studied the conditions under which different types of multicritical behaviour are realized for the O(n ) ⊕ O(n⊥) model
Summary
The concept of universality plays a paradigmatic role in the modern statistical physics. Conditions for realization of different types of multicritical behaviour, that are defined by the relation between the dimensions of the OPs n , n⊥, were obtained already in the first nontrivial approximation of the field-theoretical RG for d < 4 [8, 17, 18]. They determine the stability regions in the parametric.
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