Two-Dimensional Semi-Infinite Multicritical Ising Models

The order-parameter correlation functions of the Z 2 -invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi-infinite plane constrained to fixed or free boundary conditions. These yield the corresponding universal surface exponents which distinguish the behaviour between even- and odd-critical models. We also make explicit the interplay between duality and boundary conditions. PACS numbers 64.60.Kw, 68.35.Rh, 75.40.Cx Typeset using REVT E X Present address: Department of Physics, FM-15, University of Washington, Seattle, WA 98195, USA 1. INTRODUCTION The implications of conformal invariance of a statistical mechanical system at criticality are very powerful in two dimensions. All so-called minimal conformal field theories are completely classified, the scaling dimensions of their operators are determined and one knows in principle how to calculate all correlation functions [1,2]. From extending this work to semi-infinite system..