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arXiv · 1206.3853

Marginal dimensions for multicritical phase transitions

M. Dudka·R. Folk·Yu. Holovatch·G. Moser
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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.

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M. Dudka, R. Folk, Yu. Holovatch, G. Moser. 2012-12-26. Marginal dimensions for multicritical phase transitions. https://doi.org/10.5488/cmp.15.43001

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