Geodesic
Lattice sine-Gordon model with local Hamiltonian
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 3, pp. 364-377

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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. 
@article{TMF_1984_61_3_a3,
     author = {N. M. Bogolyubov and A. G. Izergin},
     title = {Lattice {sine-Gordon} model with local {Hamiltonian}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {364--377},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_3_a3/}
}
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N. M. Bogolyubov; A. G. Izergin. Lattice sine-Gordon model with local Hamiltonian. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 3, pp. 364-377. http://geodesic.mathdoc.fr/item/TMF_1984_61_3_a3/