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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Complete high-precision entropic sampling.

Ronald Dickman1, A G Cunha-Netto

  • 1Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil. dickman@fisica.ufmg.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2011
PubMed
Summary
This summary is machine-generated.

Tomographic entropic sampling precisely estimates configurations for statistical physics models. This novel Monte Carlo method accurately determines critical temperatures and exponents for Ising models and lattice gases.

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Area of Science:

  • Statistical Physics
  • Computational Physics
  • Thermodynamics

Background:

  • Traditional methods for estimating configurations in Monte Carlo simulations can be limited.
  • Entropic sampling offers an alternative but often requires dividing energy ranges.
  • Accurate determination of critical parameters is crucial for understanding phase transitions.

Purpose of the Study:

  • To introduce and validate tomographic entropic sampling, a new Monte Carlo scheme.
  • To achieve precise estimation of configuration counts across the entire energy spectrum.
  • To apply the method to various lattice models for critical phenomena analysis.

Main Methods:

  • Developed tomographic entropic sampling, utilizing multiple simulation starting points.
  • Applied the method to the Ising model on square and simple cubic lattices.
  • Investigated the lattice gas model with nearest-neighbor exclusion.

Main Results:

  • Achieved high accuracy (0.01%) for the critical temperature of the 2D Ising model.
  • Determined critical exponents with 1% or better precision for 2D and 3D Ising models.
  • Obtained precise critical parameters for the lattice gas model.

Conclusions:

  • Tomographic entropic sampling provides accurate and efficient estimation of configurations.
  • The method successfully determines critical properties for diverse statistical mechanics models.
  • Results are consistent across ferromagnetic and antiferromagnetic transitions and different dimensions.