Exact Results for the Adsorption of a Flexible Self-Avoiding Polymer Chain in Two Dimensions

Abstract

We derive the exact critical couplings ($x^{\ast },y_{\mathrm{a}}^{\ast }$), where $y_{\mathrm{a}}^{\ast }/x^{\ast }=\sqrt{1+\sqrt{2}}=1.533\dots$, for the polymer adsorption transition on the honeycomb lattice, along with the universal critical exponents, from the Bethe Ansatz solution of the O($n$) loop model at the special transition. Our result for the thermal scaling dimension, and thus the crossover exponent $\varphi =\frac{1}{2}$, 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 $h_{\ell +1,3}$ in the Kac formula.

11 pages, REVTEX. Minor corrections made and a new reference added to the O(n) model with mixed boundary conditions - final version for publication in Physical Review Letters

References in corpus (2)

• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Exact Theory of Polymer Adsorption in Analogy with the Kondo Problem

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