arXiv subjects

S. A. Bulgadaev

Publications and source records attributed to S. A. Bulgadaev.

22 records · Page 2Linked to original sources

arXiv1999

BKT phase transitions in two-dimensional systems with internal symmetries

The Berezinsky-Kosterlitz-Thouless (BKT) type phase transitions in two-dimensional systems with internal abelian continuous symmetries are investigated. The necessary conditions for they can take place are: 1) conformal invariance of the kinetic part of the model action, 2) vacuum manifold must be degenerated with abelian discrete homotopy group pi_1. Then topological excitations have a logarithmically divergent energy and they can be described by effective field theories generalizing the two-dimensional euclidean sine-Gordon theory, which is an effective theory of the initial XY-model. In particular, the effective actions for the two-dimensional chiral models on maximal abelian tori T_G of simple compact groups G are found. Critical properties of possible effective theories are determined and it is shown that they are characterized by the Coxeter number h_G of lattices from the series A,D,E,Z and can be interpreted as those of conformal field theories with integer central charge C=n, where n is a rank of the groups pi_1 and G. A possibility of restoration of full symmetry group G in massive phase is also dicussed.

hep-th↗

arXiv1999

On topological interpretation of quantum numbers

It is shown how one can define vector topological charges for topological exitations of non-linear sigma-models on compact homogeneous spaces T_G and G/T_G (where G is a simple compact Lie group and T_G is its maximal commutative subgroup). Explicit solutions for some cases, their energies and interaction of different topological charges are found. A possibility of the topological interpretation of the quantum numbers of groups and particles is discussed.

hep-th↗

arXiv1998

Niemeier self-dual lattices and topological phase transitions

A topological phase transition in two-dimensional nonlinear sigma-models on tori, connected with self-dual (unimodular) 24-dimensional Niemeier lattices, is considered. It is shown that critical properties of these transitions are determined by corresponding Coxeter numbers of lattices. A case of general integer-valued lattices with minimal norm equal 1 or 2 and a possible application to string theory are discussed.

hep-th↗

arXiv1998

Topological phase transitions in low-dimensional systems

A general theory of the Berezinsky-Kosterlitz-Thouless (BKT) type phase transitions in low-dimensional systems is proposed. It is shown that in d-dimensional case the necessary conditions for it can take place are 1) conformal invariance of kinetic part of model action and 2) vacuum homotopy group $π_{d-1}$ must be nontrivial and discrete. It means a discrete vacuum degeneracy for $1d$ systems and continuous vacuum degeneracy for higher $d$ systems. For such systems topological exitations have logariphmically divergent energy and they can be described by corresponding effective field theories. In general case the sufficient conditions for existence of the BKT type phase transition are 1) constraint $d \le 2$ and 2) $π_{d-1}$ must have some crystallographic symmetries. Critical properties of possible low-dimensional effective theories are determined and it is shown that in two-dimensional case they are characterized by the Coxeter numbers $h_G$ of lattices from the series ${A,D,E,Z}$ and can be interpreted as those of conformal field theories with integer central charge $c=r,$ where $r$ is a rank of groups $π_1$ and $G.$ In one-dimensional case analogous critical properties have ferromagnetic Dyson chains with discrete Cartan-Ising spins. In contrast, critical properties of one-dimensional models with periodic potentials have a weak dependence on group $G.$

hep-th↗