61 research outputs found
Periodic Ising Correlations
In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics.
II. Partition Function Evaluated by Spinor Analysis", by using representation
theory. Our approach leads to a simpler and more direct way of deriving the
spectrum of the transfer matrix for the finite periodic Ising model. We then
determine formulas for the spin correlation functions that depend on the matrix
elements of the induced rotation associated with the spin operator in a basis
of eigenvectors for the transfer matrix. The representation of the spin matrix
elements is obtained by considering the spin operator as an intertwining map.
We exhibit the "new" elements V+ and V- in the Bugrij-Lisovyy formula as part
of a holomorphic factorization of the periodic and anti-periodic summability
kernels on the spectral curve associated with the induced rotation for the
transfer matrix.Comment: 36 page
On the theory of Bose-condensate fluctuations in finite size systems
An asymptotic expansions for the grand partition function of ideal Bose gas
in the canonical ensemble with arbitrary number of particles is obtained. It is
shown that the expressions found are valid in the whole temperature region, the
critical temperature included. A comparison between the asymptotic formulas for
Bose-condensate fluctuations and the exact ones is carried out and their
quantitative agreement is established
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