Abstract:
A study is made of the Kasteleyn model, which is the simplest model of
the phase transition of two-dimensional crystalline systems into a homogeneous incommensurate phase. An exact solution of this model on
the half-plane is obtained. A dependence of the thermodynamic properties
of the system of domain walls on the distance to the boundary is found.
At small deviations $\tau$ from the critical temperature, the density of the
domain walls behaves as $\tau^{3/2}$ near the boundary and $\tau^{1/2}$ far from it.
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