A class of dual amplitudes with Mandelstam analyticity (DAMA) is studied. A detail analysis of the analytic and asymptotic properties of the amplitudes in the complex s and t plane is carried out. The role of the amplitudes for the construction of an analytic S‐matrix theory is discussed. Applications to physical processes are also presented.

We present explicit formulas for all spin matrix elements in the 2D Ising model with the nearest neighbor interaction on the finite periodic square lattice. These expressions generalize the known results [1,3,6] (coincide with them in the appropriate limits) and fulfill the test of straightforward transfer matrix calculations for finite N .

The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are obtained both for the paramagnetic and ferromagnetic regions of coupling parameter. The peculiarities caused by finite size are analyzed. The scaling limit of the lattice form factor expansion is evaluated.

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