Journal of Statistical Physics

, Volume 78, Issue 3–4, pp 681–699 | Cite as

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

  • Neal Madras


The number ofn-site lattice trees (up to translation) is believed to behave asymptotically asCn −0 λ n , 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.

Key Words

Critical exponent lattice tree lattice animal self-avoiding polygon subadditivity 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Neal Madras
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityDownsviewCanada

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