Field theory of bi- and tetracritical points: Statics

TL;DR

This paper uses renormalization group methods to analyze the static critical behavior of systems with combined symmetries, identifying fixed points and stability conditions relevant for multicritical phenomena like bicritical and tetracritical points.

Contribution

It provides a two-loop order calculation of fixed points and stability borders for systems with $O(n_ ext{||}) imes O(n_ot)$ symmetry, including the flow of static couplings and multicritical phase behavior.

Findings

Stability of the biconical fixed point for antiferromagnets in magnetic fields.

Identification of stability border lines near fixed points leading to small transient exponents.

Possibility of different multicritical behaviors depending on background parameters.

Abstract

We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability boarder lines in the space of order parameter components $n_\|$ and $n_\perp$ and spatial dimension $d$ are calculated. The essential features obtained already in two loop order for the interesting case of an antiferromagnet in a magnetic field ($n_\|=1$, $n_\perp=2$) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points leading to very small transient exponents. We are also able to calculate the flow of static couplings, which allows to consider the attraction region. Depending on the nonuniversal background parameters the existence of different multicritical behavior (bicritical or tetracritical) is possible including a triple point.