Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Dynamic Scaling near Bicritical Points

V. Dohm, Hans-Karl Janssen

Published Oct 10, 1977• 20 citations
Publisher

Abstract

We calculate by renormalized field theory, up to two-loop order, the bicritical dynamic exponents of stochastic models appropriate for describing spin-flop bicritical points. In the presence of reversible mode-coupling terms, two-loop contributions establish bicritical dynamic scaling in the restricted sense and invalidate recent predictions based on mode-coupling arguments. In case of a purely relaxational model, total bicritical dynamic scaling is found to second order in $\ensuremath{\epsilon}=4\ensuremath{-}d$.

DOI
10.1103/physrevlett.39.946

Related papers

Dynamic scaling and corrections to scaling near bicritical and tetracritical points

V. Dohm, H. K. Janssen

We study the critical dynamics of stochastic models appropriate for describing bicritical and tetracritical points in anisotropic antiferromagnetic systems. The dynamic exponents and the transient exponents are calculated by renormalized field theory up to two-loop order. In the presence of reversible mode-coupling terms, two-loop contributions establish bicritical dynamic scaling in the restricted sense and invalidate recent predictions based on mode-coupling arguments. In the case of an n-component relaxational model total dynamic scaling is found to O (ε2) both at the bicritical (n≲3) and the tetracritical (4≲n<11) points.

Journal of Applied Physics•Mar 1, 1978•6 citations

Field theory of bicritical and tetracritical points. II. Relaxational dynamics

R. Folk, Yurij V. Holovatch, G. Moser

We calculate the relaxational dynamical critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by renormalization group method within the minimal subtraction scheme in two-loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point to the dynamical stable fixed point a very small dynamic transient exponent of omega(Beta)_(v) =0.0044 is present in the dynamics for the physically important case n_|| =1 and n_perpendicular =2 in d=3 .

arXiv:0809.3146•Physical Review E•Oct 28, 2008•11 citations

Spin Flop, Supersolids, and Bicritical and Tetracritical Points

Michael Ellis Fisher, David R. Nelson

A scaling theory is introduced for bicritical points, such as antiferromagnetic spinflop points (with analogies to the upper $\ensuremath{\lambda}$ point in $^{4}\mathrm{He}$), where two distinct critical lines meet. Experimentally testable predictions follow from renormalization-group calculations which indicate that the bicritical exponents should be Heisenberg like for systems with $n\ensuremath{\le}3$ components; the crossover exponent $\ensuremath{\varphi}(\ensuremath{\simeq}1.25 \mathrm{for} n=3)$ is directly observable. For $n>3$ an intermediate ("supersolid") low-temperature phase may appear, the bicritical point then becoming tetracritical.

Physical Review Letters•Jun 17, 1974•359 citations

Field theory of bicritical and tetracritical points. IV. Critical dynamics including reversible terms

R. Folk, Yurij V. Holovatch, G. Moser

This article concludes a series of papers [Folk, Holovatch, and Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)] where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here we give the complete two-loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The nonasymptotic analysis of the dynamic flow equations shows that due to cancellation effects the critical behavior is described, in distances from the critical point accessible to experiments, by the critical behavior qualitatively found in one-loop order. Although one may conclude from the effective dynamic exponents (taking almost their one-loop values) that weak scaling for the order parameter components is valid, the flow of the time-scale ratios is quite different, and they do not reach their asymptotic values.

arXiv:1106.2026•Physical Review E•Feb 24, 2012•3 citations

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

R. Folk, Yurij V. Holovatch, G. Moser

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.

arXiv:0812.0675•Physical Review E•Mar 12, 2009•5 citations

Biconical critical dynamics

R. Folk, Yurij V. Holovatch, G. Moser

A complete two-loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in three-dimensional 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.

arXiv:1006.1766•Europhysics Letters (EPL)•Aug 1, 2010•2 citations
We calculate by renormalized field theory, up to two-loop order, the bicritical dynamic exponents of stochastic models appropriate for describing spin-flop bicritical points. In the presence of reversible mode-coupling terms, two-loop contributions establish bicritical dynamic scaling in the restricted sense and invalidate recent predictions based on mode-coupling arguments. In case of a purely relaxational model, total bicritical dynamic scaling is found to second order in \ensuremathϵ=4\ensuremath−d\ensuremath{\epsilon}=4\ensuremath{-}d\ensuremathϵ=4\ensuremath−d.
We study the critical dynamics of stochastic models appropriate for describing bicritical and tetracritical points in anisotropic antiferromagnetic systems. The dynamic exponents and the transient exponents are calculated by renormalized field theory up to two-loop order. In the presence of reversible mode-coupling terms, two-loop contributions establish bicritical dynamic scaling in the restricted sense and invalidate recent predictions based on mode-coupling arguments. In the case of an n-component relaxational model total dynamic scaling is found to O (ε2) both at the bicritical (n≲3) and the tetracritical (4≲n<11) points.
We calculate the relaxational dynamical critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by renormalization group method within the minimal subtraction scheme in two-loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point to the dynamical stable fixed point a very small dynamic transient exponent of omega(Beta)_(v) =0.0044 is present in the dynamics for the physically important case n_|| =1 and n_perpendicular =2 in d=3 .
A scaling theory is introduced for bicritical points, such as antiferromagnetic spinflop points (with analogies to the upper $\ensuremath{\lambda}$ point in 4He^{4}\mathrm{He}4He), where two distinct critical lines meet. Experimentally testable predictions follow from renormalization-group calculations which indicate that the bicritical exponents should be Heisenberg like for systems with $n\ensuremath{\le}3$ components; the crossover exponent $\ensuremath{\varphi}(\ensuremath{\simeq}1.25 \mathrm{for} n=3)$ is directly observable. For n>3n>3n>3 an intermediate ("supersolid") low-temperature phase may appear, the bicritical point then becoming tetracritical.
This article concludes a series of papers [Folk, Holovatch, and Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)] where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here we give the complete two-loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The nonasymptotic analysis of the dynamic flow equations shows that due to cancellation effects the critical behavior is described, in distances from the critical point accessible to experiments, by the critical behavior qualitatively found in one-loop order. Although one may conclude from the effective dynamic exponents (taking almost their one-loop values) that weak scaling for the order parameter components is valid, the flow of the time-scale ratios is quite different, and they do not reach their asymptotic values.
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.
A complete two-loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in three-dimensional 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.