Exact contact critical exponents of a self-avoiding polymer chain in two dimensions.

Abstract

Using previous results obtained from conformal invariance, we propose exact values in two dimensions for the contact exponents ${\mathrm{theta}}_{1}$ of one end point inside a self-avoiding polymer chain, and ${\mathrm{theta}}_{2}$ of two interior points inside the chain: ${\mathrm{theta}}_{1}$=(5/6) and ${\mathrm{theta}}_{2}$=(19/12). These values, as well as the ``limiting-ring-closure probability index'' ${\ensuremath{\Upsilon}}_{1}$ \ensuremath{\equiv}\ensuremath{\nu}(2+${\mathrm{theta}}_{1}$)=(17/8), are in excellent agreement with numerical data. They are particular cases of an infinite set of exact critical exponents for multiple contacts, which we give here.