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Journal of Statistical Physics

, Volume 86, Issue 1–2, pp 1–36 | Cite as

Monte Carlo study of the ∵-point for collapsing trees

  • N. Madras
  • E. J. Janse van Rensburg
Articles

Abstract

We investigate the collapse transition of lattice trees with nearest neighbor attraction in two and three dimensions. Two methods are used: (1) A stochastic optimization process of the Robbins-Monro type, which is designed solely to locate the maximum value of the specific heat; and (2) umbrella sampling, which is designed to sample data over a wide temperature range, as well as to combat the quasiergodicity of Metropolis algorithms in the collapsed phase. We find good evidence that the transition is second order with a divergent specific heat, and that the divergence of the specific heat coincides with the metric collapse.

Key Words

Lattice trees collapse transition scaling and crossover behavior Robbins-Monro algorithm umbrella sampling Monte Carlo 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • N. Madras
    • 1
  • E. J. Janse van Rensburg
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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