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8 - Quantum Monte Carlo methods

Published online by Cambridge University Press:  24 November 2021

David Landau  and
Kurt Binder
David Landau
Affiliation:
University of Georgia
Kurt Binder
Affiliation:
Johannes Gutenberg Universität Mainz, Germany
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Summary

In most of the discussion presented so far in this book, the quantum character of atoms and electrons has been ignored. The Ising spin models have been an exception, but since the Ising Hamiltonian is diagonal (in the absence of a transverse magnetic field), all energy eigenvalues are known and the Monte Carlo sampling can be carried out just as in the case of classical statistical mechanics. Furthermore, the physical properties are in accord with the third law of thermodynamics for Ising-type Hamiltonians (e.g. entropy S and specific heat vanish for temperature T → 0, etc.) in contrast to the other truly classical models dealt with in previous chapters (e.g. classical Heisenberg spin models, classical fluids and solids, etc.) which have many unphysical low temperature properties.

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A Guide to Monte Carlo Simulations in Statistical Physics , pp. 365 - 415
Publisher: Cambridge University Press
Print publication year: 2021

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  • Quantum Monte Carlo methods
  • David Landau, University of Georgia, Kurt Binder, Johannes Gutenberg Universität Mainz, Germany
  • Book: A Guide to Monte Carlo Simulations in Statistical Physics
  • Online publication: 24 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108780346.009
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  • Quantum Monte Carlo methods
  • David Landau, University of Georgia, Kurt Binder, Johannes Gutenberg Universität Mainz, Germany
  • Book: A Guide to Monte Carlo Simulations in Statistical Physics
  • Online publication: 24 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108780346.009
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  • Quantum Monte Carlo methods
  • David Landau, University of Georgia, Kurt Binder, Johannes Gutenberg Universität Mainz, Germany
  • Book: A Guide to Monte Carlo Simulations in Statistical Physics
  • Online publication: 24 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108780346.009
Available formats
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