Critical properties of ferromagnetic dyson chains with discrete spins

S. A. Bulgadaev

The critical properties of the one-dimensional ferromagnets with classical discrete spins interacting ∼ r -(1+σ) (1 - σ ≪ 1) in external magnetic field are investigated. Using low T expansion, relating these models with classical gases with generalized charges, the thermal and magnetic critical properties are found as for σ ≠ 1 (in first order on 1 - σ), as for σ = 1.

Satoshi Takada

Jean Zinn‐Justin, C.P. Korthals Altes, Eduardo De Rafael B +1 more

S. A. Bulgadaev

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 $G.$

K. Moorjani, T. Tanaka

Д. В. Дмитриев, V. Ya. Krivnov

Low-temperature magnetic properties of both classical and quantum dimerized ferromagnetic spin chains are studied. It is shown that at low temperatures the classical dimerized model reduces to the classical uniform model with the effective exchange integral ${J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})$, where $\ensuremath{\delta}$ is the dimerization parameter. The partition function and spin correlation function are calculated by means of mapping to the continuum limit, which is justified at low temperatures. The quantum model is studied using the Dyson-Maleev representation of the spin operators. It is shown that in the long-wavelength limit the Hamiltonian of the quantum dimerized chain reduces to that of the uniform ferromagnetic chain with the effective exchange integral ${J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})$. This fact implies that the known equivalence of the low-temperature magnetic properties of classical and quantum ferromagnetic chains remains for the dimerized chains. The considered model is generalized to include the next-neighbor antiferromagnetic interaction.