Journal of Physical Studies 13(1), Article 4003 [10 pages] (2009)
DOI: https://doi.org/10.30970/jps.13.4003

FIELD THEORETICAL APPROACH TO BICRITICAL AND TETRACRITICAL BEHAVIOR: STATICS AND DYNAMICS

R. Folk¹, Yu. Holovatch^{1,2}, G. Moser³
¹Institute for Theoretical Physics, Johannes Kepler University Linz, Altenbergerstrasse 69, A--4040, Linz, Austria
²Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine,
1 Svientsitskii St., UA--79011 Lviv, Ukraine
³Department for Material Research and Physics, Paris Lodron University Salzburg,
Hellbrunnerstrasse 34, A--5020 Salzburg, Austria

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 known 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 ($n_\|=1$, $n_\perp=2$) is 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.

PACS number(s): 05.50.+q, 64.60.Ae, 64.60.Ht