Lattice sine-Gordon model with local Hamiltonian

The excitation spectrum in the quantum lattice sine-Gordon model with Hamiltonian describing the interaction of two nearest neighbors on a lattice is obtained. This lattice model is one of the possible regularizations of the quantum field sine-Gordon model that preserve the property of complete integrability. It is shown that in the quantum field model regularized in this manner there are phase transitions at the points $\gamma=\pi n/(n+1)$ ($n$ is an integer), and these are explained by a change in the structure of the vacuum state.