Semi-infinite two-dimensional Ising model with marginally inhomogeneous couplings and conformal invariance

Abstract

The authors consider a semi-infinite two-dimensional Ising model with nearest-neighbour couplings that deviate from the bulk critical couplings by Al-2, where l is the distance from the surface. The surface critical exponents of this system are non-universal. Under a conformal mapping onto a strip of width L, the Al-1 inhomogeneity transforms into A((L/ pi )sin( pi L/L))-1. For the square lattice the spectrum of the transfer matrix in the strip geometry is calculated exactly in the extreme anisotropic limit. The analytical results and numerical results for the triangular lattice are compared with predictions of conformal invariance.