Hydrodynamics of an n-component phonon system

L. Sasvári, F. Schwabl, P. Szépfalusy

Research output: Contribution to journalArticle

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Abstract

The dynamic properties of an n-component phonon system in d dimensions, which serves as a model for a structural phase transition of second order, are investigated. The symmetry group of the hamiltonian is the group of orthogonal transformations O(n). For n ≥ 2 a continuous symmetry is broken for Tc, where Tc is the transition temperature. We derive the hydrodynamic equations for the generators of this group, the 1 2n (n - 1) angular-momentum variables. Besides the usual hydrodynamics of a phonon system, there are 1 2n (n - 1) additional independent diffusive modes for T > Tc. In the ordered phase we find 2 (n - 1) propagating modes with linear dispersion and quadratic damping. Formally the hydrodynamics is similar in the isotropic Heisenberg ferromagnet (n = 2) or the isotropic antiferromagnet (n ≥ 3). The relaxing modes for T <Tc require special care. We study the critical dynamics by means of the dynamical scaling hypothesis and by a mode-coupling calculation, both of which give the critical dynamical exponent z = 1 2d. The results are compared with the 1/n expansion. It is shown that for large n there is a non-asymptotic region characterized by an effective exponent z ̃ = φ/2ν, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.

Original languageEnglish
Pages (from-to)108-128
Number of pages21
JournalPhysica A: Statistical Mechanics and its Applications
Volume81
Issue number1
DOIs
Publication statusPublished - 1975

Fingerprint

Phonon
Hydrodynamics
Exponent
hydrodynamics
exponents
Critical Dynamics
Orthogonal Transformation
Antiferromagnet
Mode Coupling
Hydrodynamic Equations
Ferromagnet
Dynamic Properties
Correlation Length
Symmetry Group
Angular Momentum
Critical Exponents
Crossover
hydrodynamic equations
Damping
Phase Transition

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Hydrodynamics of an n-component phonon system. / Sasvári, L.; Schwabl, F.; Szépfalusy, P.

In: Physica A: Statistical Mechanics and its Applications, Vol. 81, No. 1, 1975, p. 108-128.

Research output: Contribution to journalArticle

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