Heisenberg XX chain, non-homogeneously parameterised generating exponential, and diagonally restricted plane partitions

Autor:	Malyshev, C., Bogoliubov, N. M.
Rok vydání:	2020
Předmět:	Condensed Matter - Statistical Mechanics Mathematics - Combinatorics Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
Popis:	The mean values of non-homogeneously parameterized generating exponential are obtained and investigated for the periodic Heisenberg XX model. The norm-trace generating function of boxed plane partitions with fixed volume of their diagonal parts is obtained as N-particles average of the generating exponential. The generating function of self-avoiding walks of random turns vicious walkers is obtained in terms of the circulant matrices that leads to generalizations of the Ramus's identity. Under various specifications of the generating exponential, the N-particles averages arise for a set of inconsecutive flipped spins and for powers of the first moment of flipped spins distribution at large length of the chain. These averages are expressed through the numbers of closed trajectories with constrained initial/final positions. The estimates at large temporal parameter are expressed through the numbers of diagonally restricted plane partitions characterized by fixed values of the main diagonal trace or by fixed heights of the diagonal columns in one-to-one correspondence with the flipped spins positions. Comment: 43 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.05148 Zobrazit plný text záznamu View this record from Arxiv