Abstract:
A Gaussian model on a half-axis with interaction given by a Toeptitz form is
considered. The free energy and correlation functions are calculated. A new
method of inverting Toeplitz matrices and solving the generalized Wiener-Hopf
problem is used. The asymptotic behavior of the correlation functions is studied
and the conditions for the presence or absence of long-range order are established. The free energyand correlation functions are calculated for a Gaussian model with external field. An expression is obtained for the free energy of a multidimensional Gaussian model.
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