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Journal of Experimental and Theoretical Physics Letters

Field-theoretic description of the multicritical behavior of systems with two order parameters

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Andrei A. Fedorenko

Published Dec 1, 1998• 13 citations
Publisher

Abstract

A field-theoretic description of phase transformations in complex systems with two interacting order parameters is given. For three-dimensional systems in the two-loop approximation a renormalization-group analysis of the scaling functions is carried out directly, and the fixed points corresponding to stability of the bicritical and tetracritical behavior are identified. The critical exponents at the multicritical points in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.

DOI
10.1134/1.567959

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A field-theoretic description of phase transformations in complex systems with two interacting order parameters is given. For three-dimensional systems in the two-loop approximation a renormalization-group analysis of the scaling functions is carried out directly, and the fixed points corresponding to stability of the bicritical and tetracritical behavior are identified. The critical exponents at the multicritical points in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.
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We discuss the static and dynamic multicritical behavior of three-dimensional systems of O(n∥)⊕O(n⊥)O(n_\|)\oplus O(n_\perp)O(n∥​)⊕O(n⊥​) 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∥=1n_\|=1n∥​=1, n⊥=2n_\perp=2n⊥​=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.
A field-theory description of the static and dynamic critical behavior of systems with quenched defects obeying power law correlations $\ensuremath{\sim}|\mathbf{x}{|}^{\ensuremath{-}a}$ for large separations x\mathbf{x}x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2< a< 3,2<~a<~3,2< a< 3, a renormalization analysis of the scaling functions in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behavior are identified. The obtained results essentially differ from results evaluated by a double $\ensuremath{\varepsilon},\ensuremath{\delta}$ expansion. The static and dynamic critical exponents in the two-loop approximation are calculated with the use of the Pad\'e-Borel summation technique.
We calculate the static critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by the renormalization group method within the minimal subtraction scheme in two-loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability border lines in the space of the order parameter components n_|| and n_perpendicular 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_perpendicular =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 us 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.
A field-theoretic description of the critical behaviour of systems with quenched defects obeying power law correlations ~| x | - a for large separations x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2 a 3, a renormalization analysis of the scaling function in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by a double , -expansion. The critical exponents in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.
A field-theoretic description of static and purely relaxational dynamic critical behaviour of systems with quenched defects obeying power law correlations ~| x | - a for large separations x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2 a 3, a renormalization analysis of the scaling functions in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by a double , -expansion. The static and dynamic critical exponents in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.