Pfister C.-E., Velenik Y.
Interface Pinning and Finite-Size Effects in the 2D Ising Model
(234K, uuencoded gzipped Postscript)
ABSTRACT. We apply new techniques developed in a previous work to the study of some
surface effects in the 2D Ising model. We examine in particular the
pinning-depinning transition. The results are valid for all subcritical
temperatures. By duality we obtained new finite size effects on the asymptotic
behaviour of the two-point correlation function above the critical
temperature. The key-point of the analysis is to obtain good concentration
properties of the measure defined on the random lines giving the
high-temperature representation of the two-point correlation function, as a
consequence of the sharp triangle inequality: let tau(x) be the surface
tension of an interface perpendicular to x; then for any x, y
tau(x)+tau(y)-tau(x+y) >= 1/kappa(||x||+||y||-||x+y||),
where kappa is the maximum curvature of the Wulff shape and ||x|| the Euclidean
norm of x.