Topological phase transitions in two-dimensional systems with internal symmetries

TL;DR

This paper explores generalized topological phase transitions in multicomponent 2D systems with complex symmetries, connecting various theoretical models and constructing sigma-models with topological excitations.

Contribution

It introduces new theoretical frameworks linking Ginzburg-Landau theories, sigma-models, and sine-Gordon models for systems with nontrivial homotopy groups.

Findings

Established relations between different theoretical models.

Constructed sigma-models with topological excitations.

Extended understanding of phase transitions in complex 2D systems.

Abstract

Possible generalizations of the topological (or Berezinskii-Kosterlitz-Thouless) phase transition on multicomponent 2D systems with nontrivial vector homotopic group pi_1 are considered. Relations between Ginzburg-Landau like theories, non-linear sigma-models on maximal Cartan subgroups of simple compact Lie groups and generalized sine-Gordon type theories are discussed. D-dimensional non-linear sigma-model admitting topological excitations with logarithmic energies are constructed.