The influence of a surface on Ising and conjugate model spin correlations atT=T c

Abstract

We calculate rigorously the two-point correlation function in the 2-d Ising model on a quasi-cylindrical lattice at the critical temperatureT c .The scaling predictions for the surface critical exponents η⊥ = 5/8, η∥ = 1 are confirmed and the change from surface to bulk behavior is studied. By a correspondence relation the results are mapped to the conjugate model, a subcase of the 8-vertex model. We find in this model η⊥ = 5/4, η∥ = 2.