Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (model C)

Institute for Theoretical Physics, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040, Linz, Austria.
Physical Review E (Impact Factor: 2.29). 04/2009; 79(3 Pt 1):031109. DOI: 10.1103/PhysRevE.79.031109
Source: PubMed


We calculate the relaxational dynamical critical behavior of systems of O(n_{ parallel}) plus sign in circleO(n_{ perpendicular}) symmetry including conservation of magnetization by renormalization group theory within the minimal subtraction scheme in two-loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point, strong dynamical scaling holds, with the asymptotic dynamical critical exponent z=2varphinu-1 , where varphi is the crossover exponent and nu the exponent of the correlation length. The critical dynamics at n_{ parallel}=1 and n_{ perpendicular}=2 is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen, e.g., in the temperature dependence of the magnetic transport coefficients.

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Available from: Yu. Holovatch, Jan 02, 2015
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  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 03/2009; 79(3). DOI:10.1103/PhysRevE.79.039905 · 2.81 Impact Factor
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    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. Comment: 14 pages, Submitted to the Proceedings of the Conference "Statphys'09" dedicated to the 100-th anniversary of N.N.Bogolyubov (23.06-25.06.2009, Lviv, Ukraine)
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    ABSTRACT: A complete two loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in anisotropic antiferromagnets in an external magnetic field is performed. Although strong scaling for the two order parameters (OPs) perpendicular and parallel to the field is restored as found earlier, in the experimentally accessible region the effective dynamical exponents for the relaxation of the OPs remain different since their equal asymptotic values are not reached.
    EPL (Europhysics Letters) 06/2010; DOI:10.1209/0295-5075/91/46002 · 2.10 Impact Factor
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