The long-distance asymptotics for the correlation function of the third spin components in the XXO model with interaction through two sites. (English. Russian original) Zbl 1092.82510

Zvonarev, M. B.; Izergin, A. G.; Pronko, A. G.

J. Math. Sci., New York 115, No. 1, 2002-2008 (2003); translation from Zap. Nauchn. Semin. POMI 269, 207-218 (2000).

The \(XX0\) chain in the external magnetic field directed along the \(z\) axis is discussed. The Hamiltonian describing the exchange interaction between two and four neighboring sites of the chain is constructed. An integral representation for the equal-time temperature correlation function of the third spin components is given. From the long-distance asymptotic of this correlation function, the correlation radius is calculated and its low-temperature behavior is studied.

MSC:

82B20

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics