Marginal dimensions for multicritical phase transitions

Abstract

The field-theoretical model describing multicritical phenomena with two coupled order parameters with n|| and n⊥ components and of O(n|| ⊕ O(n⊥) 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 ϵ = 4-d and to the fifth order in a pseudo-ϵ parameter using the known high-order perturbative expansions for isotropic and cubic models. Special attention is paid to a particular case of O(1) ⊕ O(2) symmetric model relevant for description of anisotropic antiferromagnets in an external magnetic field.

Keywords

• multicritical phenomena
• marginal dimensions
• renormalization group