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

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’’ ${{\rm Y}}_1$ ≡ν(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.