Condensed Matter Physics, 2006, vol. 9, No. 2(46), p. 283-304, English

Title: Homotopy in statistical physics
  R.Kenna (Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, England)

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.

Key words: homotopy, phase transitions, scaling, topological defects
PACS: 02.40.Pc, 05.20.-y, 64.60.-i, 64.70.Md, 64.70.-p

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