One-dimensional Fermi system and plane xy model

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Abstract
The behaviour of correlation functions of the one-dimensional Fermi system at large distances has been investigated by reducing it to the Sine-Gordon model. The latter is dual to the low-temperature phase of a plane xy model. In this case the fermion operator is the product of the order and disorder parameters. The transitions to the coupling constants between different states of the Fermi system states of the Fermi system may be considered as phase transitions equivalent to xy models. The elasticity modulus and spin susceptibility serves as superfluid density. The question on the phase transition of the xy model is discussed.