Hydrodynamics of an n-component phonon system

L. Sasvári, F. Schwabl and P. Szépfalusy

Physica A: Statistical Mechanics and its Applications, 1975, vol. 81, issue 1, 108-128

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 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 = 12d. 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 z̃ = φ/2ν, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.

Date: 1975
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437175900394
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:81:y:1975:i:1:p:108-128

DOI: 10.1016/0378-4371(75)90039-4

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().