Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
- Fachbereich Physik, Universitaet Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg (Germany)
The critical dynamics of relaxational stochastic models with nonconserved n-component order parameter {phi} and no coupling to other slow variables ('model A') is investigated in film geometries for the cases of periodic and free boundary conditions. The Hamiltonian H governing the stationary equilibrium distribution is taken to be O(n) symmetric and to involve, in the case of free boundary conditions, the boundary terms B{sub j}c{sub j}{phi}{sup 2}/2 associated with the two confining surface planes B{sub j}, j=1,2, at z=0 and z=L. Both enhancement variables c{sub j} are presumed to be subcritical or critical, so that no long-range surface order can occur above the bulk critical temperature T{sub c,{infinity}}. A field-theoretic renormalization-group study of the dynamic critical behavior at d=4-{epsilon} bulk dimensions is presented, with special attention paid to the cases where the classical theories involve zero modes at T{sub c,{infinity}}. This applies when either both c{sub j} take the critical value c{sub sp} associated with the special surface transition or else periodic boundary conditions are imposed. Owing to the zero modes, the {epsilon} expansion becomes ill-defined at T{sub c,{infinity}}. Analogously to the static case, the field theory can be reorganized to obtain a well-defined small-{epsilon} expansion involving half-integer powers of {epsilon}, modulated by powers of ln {epsilon}. This is achieved through the construction of an effective (d-1)-dimensional action for the zero-mode component of the order parameter by integrating out its orthogonal component via renormalization-group improved perturbation theory. Explicit results for the scaling functions of temperature-dependent finite-size susceptibilities at temperatures T{>=}T{sub c,{infinity}} and of layer and surface susceptibilities at the bulk critical point are given to orders {epsilon} and {epsilon}{sup 3/2}, respectively. They show that L dependent shifts of the multicritical special point occur along the temperature and enhancement axes. For the case of periodic boundary conditions, the consistency of the expansions to O({epsilon}{sup 3/2}) with exact large-n results is shown. We also discuss briefly the effects of weak anisotropy, relating theories whose Hamiltonian involves a generalized square gradient term B{sup kl}{partial_derivative}{sub k}{phi}{center_dot}{partial_derivative}{sub l}{phi} to those with a conventional ({nabla}{phi}){sup 2} term.
- OSTI ID:
- 21192550
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 79, Issue 10; Other Information: DOI: 10.1103/PhysRevB.79.104301; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
Similar Records
Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
Intense nonneutral beam propagation through a periodic focusing quadrupole field II--Hamiltonian averaging techniques in the smooth-focusing approximation
Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANISOTROPY
BOUNDARY CONDITIONS
COUPLING
CRITICAL TEMPERATURE
DISTRIBUTION
EXPANSION
FIELD THEORIES
FILMS
HAMILTONIANS
LAYERS
ONE-DIMENSIONAL CALCULATIONS
ORDER PARAMETERS
PERIODICITY
PERTURBATION THEORY
RENORMALIZATION
SCALING
SIMULATION
STOCHASTIC PROCESSES
SURFACES
TEMPERATURE DEPENDENCE