SURFACE CRITICAL-BEHAVIOR OF AN O(N) LOOP MODEL RELATED TO 2 MANHATTAN LATTICE WALK PROBLEMS

We find and discuss the scaling dimensions of the branch 0 manifold of the Nienhuis O(n) loop model an the square lattice, concentrating on the surface dimensions. The results are extracted from a Bethe ansatz calculation of the finite-size corrections to the eigenspectrum of the six-vertex model with free boundary conditions. These results are especially interesting for polymer physics at two values of the crossing parameter lambda. Interacting self-avoiding walks on the Manhattan lattice at the collapse temperature (lambda = pi/3) and Hamiltonian walks on the Manhattan lattice (lambda = pi/2) are discussed in detail. Our calculations illustrate the importance of examining both odd and even strip widths when performing finite-size correction calculations to obtain scaling dimensions.