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Conventional and Unconventional Numerical Transfer-Matrix Methods

Published online by Cambridge University Press:  26 February 2011

M. A. Novotny  and
P. A. Rikvold
M. A. Novotny
Affiliation:
Supercomputer Computations Research Institute, B-186, Florida State University, Tallahassee, Florida 32306
P. A. Rikvold
Affiliation:
Physics Department and Center for Materials Research and Technology, B-159, Florida State University, Tallahassee, Florida 32306
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Abstract

We briefly review the numerical transfer-matrix (TM) method and its application to materials science. We report on the conventional use of TM methods to calculate phase diagrams and critical exponents of classical statistical mechanical models in d=2. Examples presented here are spin-1/2 and spin-1 models (two- and three-state lattice-gas models). Discussed are a model for oxygen -ordering in the high temperature superconductor YBa2Cu3O6+x and a model for the electrosorption of an organic substance on a metal. Some results for the spin-1/2 model in d=3 are also presented. Three unconventional applications of the TM method will also be reported. These include a study of the surface tension of spin-1/2 models, a TM formalism for metastability, and a study of a translationally invariant (non-fractal) spin-1/2 model in non-integer dimensions.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 278: Symposium W – Computational Methods in Materials Science , 1992 , 15
Copyright
Copyright © Materials Research Society 1992

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