Geodesic
Rigorous results of phase transition theory in lattice boson models
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 335-343

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Quantum systems of particles obeying Bose statistics and moving in $d$-dimensional lattices are studied. The original Bose–Hubbard Hamiltonian is considered, together with model systems related to this Hamiltonian: the Bose–Hubbard model with exchange interaction of infinite radius and the Bose–Hubbard model with infinite interaction potential. Rigorous results concerning the proof of the existence of Bose condensation and a phase transition to the Mott insulator state in these systems are presented. 
@article{TRSPY_2015_290_a27,
     author = {D. P. Sankovich},
     title = {Rigorous results of phase transition theory in lattice boson models},
     journal = {Informatics and Automation},
     pages = {335--343},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a27/}
}
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D. P. Sankovich. Rigorous results of phase transition theory in lattice boson models. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 335-343. http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a27/