Geodesic
Free energy of an anharmonic crystal
Teoretičeskaâ i matematičeskaâ fizika, Tome 12 (1972) no. 1, pp. 135-146

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The method of two-time Green's functions is used to obtain an expression for the free energy as a cumulant expansion in irreducible correlation functions; this is represented as an expansion in the renormalized anharmonic interaction. A selfeonsistent approach to the calculation of the free energy is considered and a closed expression is obtained for it in the second order in the interaction. 
@article{TMF_1972_12_1_a11,
     author = {N. M. Plakida},
     title = {Free energy of an anharmonic crystal},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {135--146},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_12_1_a11/}
}
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N. M. Plakida. Free energy of an anharmonic crystal. Teoretičeskaâ i matematičeskaâ fizika, Tome 12 (1972) no. 1, pp. 135-146. http://geodesic.mathdoc.fr/item/TMF_1972_12_1_a11/