Condensed Matter Physics, 2006, vol. 9, No. 2(46), p. 283-304, English
Homotopy in statistical physics
(Applied Mathematics Research Centre, Coventry University,
Coventry, CV1 5FB, England)
In condensed matter physics and related areas,
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.
homotopy, phase transitions, scaling, topological
02.40.Pc, 05.20.-y, 64.60.-i, 64.70.Md, 64.70.-p