The applicability of certain Monte Carlo methods to the analysis of interacting polymers

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The authors consider polymers, modeled as self-avoiding walks with interactions on a hexagonal lattice, and examine the applicability of certain Monte Carlo methods for estimating their mean properties at equilibrium. Specifically, the authors use the pivoting algorithm of Madras and Sokal and Metroplis rejection to locate the phase transition, which is known to occur at {beta}{sub crit} {approx} 0.99, and to recalculate the known value of the critical exponent {nu} {approx} 0.58 of the system for {beta} = {beta}{sub crit}. Although the pivoting-Metropolis algorithm works well for short walks (N < 300), for larger N the Metropolis criterion combined with ... continued below

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150 p.

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Krapp, D.M. Jr. May 1, 1998.

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The authors consider polymers, modeled as self-avoiding walks with interactions on a hexagonal lattice, and examine the applicability of certain Monte Carlo methods for estimating their mean properties at equilibrium. Specifically, the authors use the pivoting algorithm of Madras and Sokal and Metroplis rejection to locate the phase transition, which is known to occur at {beta}{sub crit} {approx} 0.99, and to recalculate the known value of the critical exponent {nu} {approx} 0.58 of the system for {beta} = {beta}{sub crit}. Although the pivoting-Metropolis algorithm works well for short walks (N < 300), for larger N the Metropolis criterion combined with the self-avoidance constraint lead to an unacceptably small acceptance fraction. In addition, the algorithm becomes effectively non-ergodic, getting trapped in valleys whose centers are local energy minima in phase space, leading to convergence towards different values of {nu}. The authors use a variety of tools, e.g. entropy estimation and histograms, to improve the results for large N, but they are only of limited effectiveness. Their estimate of {beta}{sub crit} using smaller values of N is 1.01 {+-} 0.01, and the estimate for {nu} at this value of {beta} is 0.59 {+-} 0.005. They conclude that even a seemingly simple system and a Monte Carlo algorithm which satisfies, in principle, ergodicity and detailed balance conditions, can in practice fail to sample phase space accurately and thus not allow accurate estimations of thermal averages. This should serve as a warning to people who use Monte Carlo methods in complicated polymer folding calculations. The structure of the phase space combined with the algorithm itself can lead to surprising behavior, and simply increasing the number of samples in the calculation does not necessarily lead to more accurate results.

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150 p.

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OSTI as DE98056107

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  • Other Information: DN: Paper submitted to Univ. of California, Berkeley, CA (US); TH: Thesis (Ph.D.)

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  • Other: DE98056107
  • Report No.: LBNL--41775
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 674710
  • Archival Resource Key: ark:/67531/metadc703376

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  • May 1, 1998

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  • Sept. 12, 2015, 6:31 a.m.

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  • June 14, 2016, 8:28 p.m.

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Krapp, D.M. Jr. The applicability of certain Monte Carlo methods to the analysis of interacting polymers, thesis or dissertation, May 1, 1998; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc703376/: accessed June 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.