Geodesic
Description of~Gibbs random fields by~the generating functional method
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 383-391

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It is proved that generating functionals of a large class of systems with binary interactions determine the probability measures on the configuration space of infinite system. In this class of measures the Bogoliubov equation for the generating functional and the Dobrushin–Lanford–Ruelle equation for the measure are equivalent to each other. 
@article{TMF_1980_42_3_a8,
     author = {G. I. Nazin},
     title = {Description {of~Gibbs} random fields by~the generating functional method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {383--391},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a8/}
}
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G. I. Nazin. Description of~Gibbs random fields by~the generating functional method. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 383-391. http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a8/