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Monte Carlo Methods

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Computational Materials Science

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 129))

Abstract

Nature is composed of gross assemblies of huge numbers of atoms and molecules showing a wide variety of phenomena according to the way how they are assembling. The macroscopic behaviors of such systems are rather different from the microscopic laws in the world of atoms and molecules. For example, in the usual cases of macroscopic systems, the motion of the atoms and molecules can be regarded simply as heat. That is, the average kinetic energy of each atom and molecule in a macroscopic system is equal to a quantity measured as the temperature. The other contributor to macroscopic behavior is the cooperative motion of atoms and molecules (or sometimes electrons). Since atoms and molecules interact with each other, their macroscopic assemblies can have cooperative motions. Many examples can be seen in our daily life: spring or rubber elasticity, magnetization in permanent magnets, shape memory alloys, liquid flows, surface tension of liquids, swelling of polymers by water absorption, etc. Sometimes such cooperative motions are frozen as the temperature decreases. In this case, the states which have been realized at higher temperatures become unstable. This phenomenon is called a phase transition [1,2]. For example, ferromagnets show nonzero magnetization below the Curie temperature, and superconductors show zero resistivity below a certain temperature called the critical temperature. These phase transitions accompany a spontaneous symmetry breakdown (i.e. the breakdown of symmetry in the spin direction in magnets or in the electric gauge in superconductors) and do not produce latent heat or a volume change at the transition temperature.

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  1. Institute for Materials Research, Tohoku University, 980-8577, Sendai, Japan

    Prof. Kaoru Ohno, Dr. Keivan Esfarjani & Prof. Yoshiyuki Kawazoe

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Ohno, K., Esfarjani, K., Kawazoe, Y. (1999). Monte Carlo Methods. In: Computational Materials Science. Springer Series in Solid-State Sciences, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59859-3_5

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