An equivalence relation of boundary/initial conditions, and the infinite limit properties

Details An equivalence relation of boundary/initial conditions, and the infinite limit properties An equivalence relation of boundary/initial conditions, and the infinite limit properties

2005-03-08

arxiv.org/abs/cond-mat/0503192v2

J.Phys.Soc.Jpn.74 (2005)1640-1641

Physics

Condensed Matter

Statistical Mechanics

6 pages with a figure, no change but the omitted figure is added

Scientific paper

10.1143/JPSJ.74.1640

The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex model is classified through the density of left/down arrows on the boundary. The free energy becomes identical to that obtained by Lieb and Sutherland with the periodic boundary condition, if the density of the arrows is equal to 1/2. The relation to the structure of the transfer matrix and a relation to stochastic processes are noted.

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