论文信息 - A rigorous bound on the critical exponent for the number of lattice trees, animals, and polygons

A rigorous bound on the critical exponent for the number of lattice trees, animals, and polygons

The number ofn-site lattice trees (up to translation) is believed to behave asymptotically asCn−0λn, where θ is a critical exponent dependent only on the dimensiond of the lattice. We present a rigorous proof that θ≥(d−1)/d for anyd≥2. The method also applies to lattice animals, site animals, and two-dimensional self-avoiding polygons. We also prove that θ≧v whend=2, wherev is the exponent for the radius of gyration.

Neal Madras

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