2020/11/10 by C. Malyshev, Malyshev, C., N. M. Bogoliubov +1
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2011.05148
openalex publication_date 2020/11/10 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
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.