Dynamic critical properties of a stochastic n-vector model

L. Sasvári, P. Szépfalusy

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Abstract

A stochastic model is introduced with a non-conserved order parameter of n real components coupled to the density of generators for the rotation of the order parameter. As microscopic background it is based on a lattice dynamic model with O(n) symmetry. In the symmetry breaking phase a rearranged perturbation scheme is introduced in which the response and correlation functions are expressed in terms of new blocks free from the singularities of the self-energies. It is shown that the transverse fluctuations of the order parameter and the fluctuations of that component of the generator field which rotates the order parameter around its equilibrium position have common excitation spectra. The dynamic renormalization group is applied to the model in a form somewhat different from those introduced earlier. A detailed analysis is carried out to O(ε{lunate}). Though the stable fixed point for d < 4 depends on n it leads to the dynamic critical exponent z = 1 2d for all values of n. In the hydrodynamic region above Tc the excitation spectra turn out to be independent of n to O(ε{lunate}). Consequences of the energy conservation and anisotropy are discussed.

Original languageEnglish
Pages (from-to)1-34
Number of pages34
JournalPhysica A: Statistical Mechanics and its Applications
Volume87
Issue number1
DOIs
Publication statusPublished - Apr 1977

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ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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