Erich Eisenriegler

Conformal theory of energy correlations in the semi-infinite two-dimensional O(N) model

Abstract With conformal-invariance methods we calculate the energy-energy correlation function of the semi-infinite two-dimensional O(N) model with −2 ⩽ N ⩽ 2. Boundary conditions corresponding to ordinary, extraordinary, and special surface critical behaviour are considered. The crossover exponent φ of the special transition has the value φ = 1 2 . Particular attention is given to the limit N → 0, corresponding to the self-avoiding walk or polymer.

Conformal theory of the two-dimensional O(N) model with ordinary, extraordinary, and special boundary conditions

Abstract The two-dimensional critical O( N ) model with ordinary, extraordinary, and special boundary conditions is analyzed with conformal-invariance methods. Contrary to an earlier conjecture, the energy density does not vanish at an edge with special boundary conditions. Exact expressions for the energy-energy correlation function in the half-space are given for all three boundary conditions. For several sets of mixed boundary conditions the Casimir contribution to the free energy in the strip geometry and the profile of the energy density are calculated.

Universal order-parameter profiles in confined critical systems with boundary fields

The authors consider systems at the bulk critical temperature with an ordering field applied at the boundary. For various boundary geometries, universal expressions for the spatial dependence of the order parameter are obtained by conformal mapping of the known results for the half space. Analytical results for strip, wedge and other two-dimensional geometries and for systems with spherical boundaries in arbitrary dimension are given.