Exact results for the adsorption of a flexible self-avoiding polymer chain in two dimensions

We derive the exact critical couplings (x*,ya*), where ya*/x*=1+2 =1.533, for the polymer adsorption transition on the honeycomb lattice, along with the universal critical exponents, from the Bethe ansatz solution of the On loop model at the special transition. Our result for the thermal scaling dimension, and thus the crossover exponent =12, is in agreement with an earlier result based on conformal invariance arguments. Our result for the geometric scaling dimensions confirms recent conjectures that they are given by h+1,3 in the Kac formula.