M. Dudka, R. Folk, Yu. Holovatch, G. Moser
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 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 known high-order expansions for isotropic and cubic models. Special attention is paid to particular case of $O(1){\oplus} O(2)$ symmetric model relevant for anisotropic antiferromagnets in an external magnetic field.
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http://arxiv.org/abs/1206.3853
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