Exact Theory of Polymer Adsorption in Analogy with the Kondo Problem

TL;DR

This paper develops an exact scaling theory for 2D polymer adsorption using boundary S matrices, connecting it to the Kondo problem and providing detailed critical exponents and phase transition insights.

Contribution

It introduces an exact theoretical framework for polymer adsorption in 2D, linking it to the Kondo problem and solving the special transition in the O(n) model.

Findings

Computed boundary free energy and crossover exponent.

Analyzed flow from adsorbed to desorbed phase.

Identified the n=2 limit as equivalent to the Kondo problem.

Abstract

We conjecture the exact scaling theory for the adsorption of two-dimensional polymers by using boundary S matrices. We compute the boundary free energy (the ``g-function''), study the flow from adsorbed to desorbed phase, and derive the crossover exponent and all the geometrical exponents at the transition. More generally, we solve the special transition in the O(n) model, the polymer case corresponding to n=0. The n=2 limit appears identical to the ordinary Kondo problem.