>>46

Berezinskiiは、topologyに言及していないが、Kosterlitz, J. M.; Thouless, D. J.では、topological invariant を使っている
http://mecklenburg.bol.ucla.edu/kosterlitz%20and%20thouless%20transistion.pdf
^ Kosterlitz, J. M.; Thouless, D. J. (1973). “Ordering, metastability and phase transitions in two-dimensional systems”. Journal of Physics C: Solid State Physics 6 (7): 1181-1203. Bibcode 1973JPhC....6.1181K. doi:10.1088/0022-3719/6/7/010.
(抜粋)
Abstract. A new definition of order called topological order is proposed for two-dimensional
systems in which no long-range order of the conventional type exists. The possibility of a
phase transition characterized by a change in the response of the system to an external
perturbation is discussed in the context of a mean field type of approximation. The critical
behaviour found in this model displays very weak singularities. The application of these
ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid
are discussed. This type of phase transition cannot occur in a superconductor nor in a
Heisenberg ferromagnet. for reasons that are given.
つづく