Field Theoretical Approach to Bicritical and Tetracritical Behavior: Static and Dynamics

TL;DR

This paper uses field theoretical renormalization group methods to analyze static and dynamic multicritical behavior in three-dimensional systems with $O(n_ ext|) imes O(n_ot)$ symmetry, providing refined quantitative descriptions and exploring dynamical critical exponents.

Contribution

It offers a detailed two-loop analysis of static multicritical points and extends the study to dynamical behavior with various critical dynamics forms.

Findings

Stable biconical fixed point for antiferromagnets in a magnetic field

Small transient exponents near stability border lines

Quantitative dynamical critical exponents calculated

Abstract

We discuss the static and dynamic multicritical behavior of three-dimensional systems of $O(n_\|)\oplus O(n_\perp)$ symmetry as it is explained by the field theoretical renormalization group method. Whereas the static renormalization group functions are currently know within high order expansions, we show that an account of two loop contributions refined by an appropriate resummation technique gives an accurate quantitative description of the multicritical behavior. One of the essential features of the static multicritical behavior 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 further pursue an analysis of dynamical multicritical behavior choosing different forms of critical dynamics and calculating asymptotic and effective dynamical exponents within the minimal subtraction scheme.