Geodesic
Solvability of the system of integral equations of lattice models of statistical mechanics
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 10-24

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The paper is a review of results on the solvability of a system of integral equations, which is an analog of the Kirkwood–Salzburg equations for an infinite set of partial probability distributions of Gibbs random sets on $\mathbb{Z}^d$ corresponding to lattice gas models of equilibrium statistical mechanics with a pair interaction potential $U$. We study the relationship between the solvability of the system and the location of zeros of the partition functions $Q_\Lambda(z)$ of models.
Keywords: statistical mechanics, Gibbs distribution, lattice system, Kirkwood–Salzburg equations, partition function, thermodynamic limit. 
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     author = {Yu. P. Virchenko},
     title = {Solvability of the system of integral equations of lattice models of statistical mechanics},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {10--24},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a1/}
}
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Yu. P. Virchenko. Solvability of the system of integral equations of lattice models of statistical mechanics. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 10-24. http://geodesic.mathdoc.fr/item/INTO_2021_195_a1/