Marriage of exact enumeration and 1/d expansion methods: Lattice model of dilute polymers

We consider the properties of a self-avoiding polymer chain with nearestneighbor contact energyɛ on ad-dimensional hypercubic lattice. General theoretical arguments enable us to prescribe the exact analytic form of then-segment chain partition functionCn,and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data ind=2–6. This exact form provides the main ingredient to produce a large-n expansion ind−1of the chain free energy through fifth order with the full dependence on the contact energy retained. The ɛ-dependent chain connectivity constant and free energy amplitude are evaluated within thed−1expansion toO(d−5). Our general formulation includes for the first time self-avoiding walks, neighboravoiding walks, theta, and collapsed chains as particular limiting cases.

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