Journal of Physical Studies 4(4), 409–414 (2000) DOI: https://doi.org/10.30970/jps.04.409 ANALYTICAL PROPERTIES OF THE PROPAGATOR IN THE EXACTLY SOLVABLE QUANTUM FIELD THEORY O. O. Lisovy Taras Shevchenko Kyiv National University, Department of Physics, 6 acad. Glushkova Pr., Kyiv, UA-03022, Ukraine

The quantum field theory interpretation of the exact solution of 2$D$ Ising model is given. The momentum representation of the two-point correlation function is obtained and its analytic continuation on the time-like region $(p^2<0)$ is fulfilled. It is shown that the propagator corresponding to the Ising model paramagnetic phase has the simple pole at $p^2=-m^2$ and the logarithmic branch points at $p^2=-9m^{2}$, $-25m^{2}$, $… $. These branch points correspond to the thresholds of the creation of $n$-particles intermediate states. Threshold and asymptotic behaviour of the propagator's discontinuity is evaluated.

PACS number(s): 05.50.+q, 11.10.-z

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