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DY: Dynamik und Statistische Physik

DY 37: Critical phenomena and phase transitions II

DY 37.3: Vortrag

Mittwoch, 26. März 2003, 17:00–17:15, G\"OR/229

Surface critical behavior at m-axial Lifshitz points — •Hans Werner Diehl, Anja Gerwinski, and Sergej Rutkevich — Fachbereich Physik, U. Essen, D-45117 Essen

The critical behavior of semi-infinite d-dimensional systems with short-range interactions and an n-component order parameter is investigated at an m-axial (bulk) Lifshitz point whose wave-vector instability occurs in an m-dimensional isotropic subspace of IR^m. The associated m modulation axes are presumed to be parallel to the surface, where 0≤ m≤ d−1. An appropriate n-component semi-infinite φ⁴ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that besides boundary terms of the kind known from the m=0 case of the usual semi-infinite φ⁴ model, a further boundary term, involving a dimensionless coupling constant λ, must be included in the Hamiltonian. The fixed points describing the ordinary, special, and extraordinary transitions below the upper critical dimension d^*(m)=4+m/2 are identified, and results of a two-loop RG analysis for the ordinary transition are presented.The corresponding surface critical exponent β₁^ord, and other surface exponents related to it (and bulk exponents) are computed to second order in є=d−d^*(m). These series expansions are utilized to estimate the values of such exponents for d=3, which are then compared with recent Monte Carlo estimates. Finally, we show that the scaling dimension of the surface energy density can be determined exactly.