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Monte Carlo Simulation

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Book cover Springer Handbook of Metrology and Testing

Part of the book series: Springer Handbooks ((SHB))

Abstract

In the general overview on materials and their characteristics, outlined in Sect. 1.3, it has been stated that materials and their characteristics result from the processing of matter. Thus, condensed matter physics is one of the fundamentals for the understanding of materials. The Monte Carlo Method, which is a powerful method in this respect, is presented in this final chapter of the Handbookʼs Part E on Modelling and Simulation Methods as follows:

First, the principles of this simulation technique are introduced

  • Monte Carlo Method: the fundamentals

  • Improved Monte Carlo algorithms

  • Quantum Monte Carlo Method.

Second, the application of the Monte Carlo Method is explained in considering selected areas of materials science.

  • Electronic correlations: antiferromagnetism

  • Perfect conductance of electricity: superconductivity

  • Vortex states in condensed matter physics

  • Quantum critical phenomena.

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Abbreviations

AF:

antiferromagnetism

BBG:

Bragg–Bose glass

BG:

Bose glass

DMRG:

density-matrix renormalization group

DOS:

density of states

GFSR:

generalized feedback shift register

GL:

Ginzburg–Landau

IL:

interstitial liquid

KT:

Kosterlitz–Thouless

LD:

Lawrence–Doniach

LD:

laser device

LD:

laser diode

MC:

Monte Carlo

MD:

molecular dynamics

PIRG:

path-integral renormalization group

RG:

renormalization group

SC:

superconductivity

SSE:

stochastic series expansion

SW:

Swendsen–Wang

TGFSR:

twisted GFSR

VG:

vortex glass

VL:

vortex liquid

WZW:

Wess–Zumino–Witten

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  1. World Premier International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Namiki 1-1, 305-0044, Tsukuba, Japan

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  2. Computational Materials Science Center, National Institute for Materials Science, Sengen 1-2-1, Tsukuba, 305-0047, Ibaraki, Japan

    Yoshihiko Nonomura Ph.D.

  3. Computational Materials Science Center, National Institute for Materials Science, 1-2-1 Sengen, 305-0047, Tsukuba, Japan

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Hu, X., Nonomura, Y., Kohno, M. (2011). Monte Carlo Simulation. In: Czichos, H., Saito, T., Smith, L. (eds) Springer Handbook of Metrology and Testing. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16641-9_22

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