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Renormalized multicanonical sampling in multiple dimensions.

Yong Hwan Lee1, David Yevick1

  • 1Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G7.

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|November 15, 2016
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Summary
This summary is machine-generated.

This study enhances a multicanonical sampling method for calculating system density of states. The improved procedure shows increased efficiency and accuracy, especially for larger systems like the Ising model.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics

Background:

  • The renormalized multicanonical sampling procedure offers a way to determine system density of states from smaller systems.
  • Enhancements are needed to improve accuracy and efficiency for complex systems.

Purpose of the Study:

  • To extend the renormalized multicanonical sampling procedure to two and three dimensions.
  • To enhance the method's accuracy and efficiency using a transition matrix Monte Carlo approach.
  • To evaluate the performance of the enhanced procedure on the Ising model.

Main Methods:

  • Extension of the renormalized multicanonical sampling procedure to higher dimensions.
  • Integration of a transition matrix Monte Carlo method with multicanonical sampling.
  • Calculation of specific heat for Ising models on square and cubic lattices.

Main Results:

  • The enhanced procedure demonstrates improved accuracy and efficiency.
  • Performance was tested on Ising models up to 128^2 and 24^3 spins.
  • The relative advantage of the renormalized procedure grows with system size.

Conclusions:

  • The extended and enhanced multicanonical sampling procedure is effective for large-scale simulations.
  • The method provides a significant advantage over existing transition matrix Monte Carlo algorithms for larger systems.
  • This approach is valuable for studying the density of states in complex physical systems.