Homotopy in statistical physics

Details Homotopy in statistical physics Homotopy in statistical physics

2006-02-20

arxiv.org/abs/cond-mat/0602459v2

Condensed Matter Phys.9:283-304,2006

Physics

Condensed Matter

Statistical Mechanics

Significant extensions and updates: 29 pages, 11 figures. Lecture given at the Mochima Spring School, Mochima, Venezuela, June

Scientific paper

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction to the mathematical methods involved in topology and homotopy theory, the role of the latter in a number of mainly low-dimensional statistical-mechanical systems is outlined. Some recent activities in this area are reviewed and some possible future directions are discussed.

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