Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-12-06
St.-Petersburg Mathematical Journal, Vol. 22, No. 3 (2011), 359-377
Physics
Condensed Matter
Statistical Mechanics
22 pages, 1 figure, LaTeX
Scientific paper
The XXZ Heisenberg chain is considered for two specific limits of the anisotropy parameter: $\Dl\to 0$ and $\Dl\to -\infty$. The corresponding wave functions are expressed by means of the symmetric Schur functions. Certain expectation values and thermal correlation functions of the ferromagnetic string operators are calculated over the base of N-particle Bethe states. The thermal correlator of the ferromagnetic string is expressed through the generating function of the lattice paths of random walks of vicious walkers. A relationship between the expectation values obtained and the generating functions of strict plane partitions in a box is discussed. Asymptotic estimate of the thermal correlator of the ferromagnetic string is obtained in the limit of zero temperature. It is shown that its amplitude is related to the number of plane partitions.
Bogoliubov Nikolay M.
Malyshev C.
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