Correlation length in Ising strips with free and fixed boundary conditions

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Abstract
The correlation length of boundary spins in the Ising model, defined on strips of triangular lattice with free boundary conditions, is determined with an efficient numerical procedure based on the star-triangle transformation. In the case of isotropic critical interactions, the extrapolated amplitude of the correlation length is in excellent agreement with the value 2/( pi eta /sub ///) predicted by conformal invariance. An analytical formula for the amplitude in strips with anisotropic interactions is proposed. Fixing the spins on one edge reduces the amplitude of the correlation length on the other edge by a factor 1/2. The convergence of phenomenological renormalisation with free boundary conditions is studied.