### Abstract

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.

Original language | English |
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Pages (from-to) | 283-304 |

Journal | Condensed Matter Physics |

Volume | 9 |

Issue number | 2(46) |

DOIs | |

Publication status | Published - 2006 |

### Bibliographical note

The full text is available from: http://dx.doi.org/10.5488/CMP.9.2.283### Keywords

- homotopy
- phase transitions
- scaling
- topological defects

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## Cite this

Kenna, R. (2006). Homotopy in statistical physics.

*Condensed Matter Physics*,*9*(2(46)), 283-304. https://doi.org/10.5488/CMP.9.2.283