Marginal dimensions for multicritical phase transitions

TL;DR

This paper analyzes the conditions and stability regions for various multicritical behaviors in models with coupled order parameters using advanced renormalization group techniques.

Contribution

It provides a detailed field-theoretical analysis of multicritical phenomena with two coupled order parameters, including stability surfaces and marginal dimensions up to high perturbative orders.

Findings

Calculated stability surfaces in parametric space for multicritical behavior.

Derived series for marginal dimensions controlling crossover between universality classes.

Special analysis of O(1) up O(2) model relevant for anisotropic antiferromagnets.

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.