Surface free energy of the critical six-vertex model with free boundaries

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Abstract
The Bethe ansatz equations are derived for the six-vertex model with general boundary weights on a lattice in a diagonal orientation. These are solved in the thermodynamic limit. Finite-size corrections to the free energy (for a restricted class of boundary weights, including those corresponding to a Potts model with free boundaries) are calculated in the critical region. The first-order term gives the surface free energy of the model. The second-order term is found to be - pi okT tan( pi nu /2 mu )c/48N'2 where c=(1-6 mu 2/( pi 2- pi mu )) is the conformal anomaly. This can be compared to - pi kT sin( pi nu / mu )c/6N'2 for a calculation on the lattice in the standard orientation and with periodic boundary conditions. This difference can be explained geometrically using conformal invariance.