\(XXO\) Heisenberg chain and random walks. (Russian, English) Zbl 1080.60090

Bogolyubov, N. M.

Zap. Nauchn. Semin. POMI 325, 13-27 (2005); translation in J. Math. Sci., New York 138, No. 3, 5636-5643 (2006).

The author shows that one can consider the time-dependent correlation functions of the \( XXO \) Heisenberg chain as the generating functions of random walks on a one-dimensional lattice. The explicit forms of correlation functions on infinite, semi-infinite and finite lattices are obtained. The long time asymptotic behaviour of these functions is studied.

Reviewer: Nasir N. Ganikhodjaev (Kuala Lumpur)

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
05E10	Combinatorial aspects of representation theory
82B20	Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60G50	Sums of independent random variables; random walks

Keywords:

correlation functions