Some results on hyperscaling in the 3D Ising model

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The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length ... continued below

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9 p.

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Baker, G.A. Jr. & Kawashima, Naoki September 1, 1995.

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The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length L, divided by L. They also find that {zeta}{sub L}/L {ge} 0.26 is definitely too large for reliable studies of the critical value, g*, of the renormalized coupling constant. They have reasonable evidence that {zeta}{sub L}/L {approx} 0.1 is adequate for results that are within one percent of those for the infinite system size. On this basis, they have conducted a series of Monte Carlo calculations with this condition imposed. These calculations were made practical by the development of improved estimators for use in the Swendsen-Wang cluster method. The authors found from these results, coupled with a reversed limit computation (size increases with the temperature fixed at the critical temperature), that g* > 0, although there may well be a sharp downward drop in g as the critical temperature is approached in accord with the predictions of series analysis. The results support the validity of hyperscaling in the 3 dimensional Ising model.

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9 p.

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OSTI as DE95017012

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  • Hayashibara forum `95, Kyoto (Japan), Jul 1995

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  • Other: DE95017012
  • Report No.: LA-UR--95-2506
  • Report No.: CONF-9507156--1
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 102238
  • Archival Resource Key: ark:/67531/metadc619200

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  • September 1, 1995

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • March 1, 2016, 1:51 p.m.

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Baker, G.A. Jr. & Kawashima, Naoki. Some results on hyperscaling in the 3D Ising model, article, September 1, 1995; New Mexico. (digital.library.unt.edu/ark:/67531/metadc619200/: accessed November 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.