Geodesic
Distribution of dimers on a plane square lattice in the Percus–Yevick approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 387-394 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The total and direct correlation matrices of the distribution of dimers on a square lattice are calculated in the Percus–Yevick approximation. The solution that correctly describes the thermodynamic behavior of a lattice gas of dimers is distinguished among several solutions of the system of equations for the elements of the direct correlation matrix. The difference between the thermodynamic functions calculated by means of this solution and the functions found by extrapolating the power-law expansions becomes appreciable only near the closely packed state of the lattice gas and in this region does not exceed $6\%$. 
@article{TMF_1981_47_3_a9,
     author = {E. V. Aksenenko and Yu. V. Shulepov},
     title = {Distribution of dimers on a~plane square lattice in the {Percus{\textendash}Yevick} approximation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {387--394},
     year = {1981},
     volume = {47},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a9/}
}
TY  - JOUR
AU  - E. V. Aksenenko
AU  - Yu. V. Shulepov
TI  - Distribution of dimers on a plane square lattice in the Percus–Yevick approximation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1981
SP  - 387
EP  - 394
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a9/
LA  - ru
ID  - TMF_1981_47_3_a9
ER  - 
%0 Journal Article
%A E. V. Aksenenko
%A Yu. V. Shulepov
%T Distribution of dimers on a plane square lattice in the Percus–Yevick approximation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1981
%P 387-394
%V 47
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a9/
%G ru
%F TMF_1981_47_3_a9
E. V. Aksenenko; Yu. V. Shulepov. Distribution of dimers on a plane square lattice in the Percus–Yevick approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 387-394. http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a9/

[1] Guggenheim E. A., Mixtures, Clarendon, Oxford, 1952

[2] Montroll E. V., Prikladnaya kombinatornaya matematika, Sb., ed. Bekkenbakh E., Mir, M., 1968, Statistika reshetok

[3] Kasteleyn P. W., “Dimer statistics and phase transitions”, J. Math. Phys., 4:2 (1963), 287–293 | DOI | MR

[4] Temperley H. N. V., Fisher M. E., “Dimer problem in statistical mechanics - an exact result”, Phil. Mag., 6:68 (1961), 1061–1063 | DOI | MR | Zbl

[5] Kasteleyn P. W., “The statistics of dimers on a lattice. 1: The number of dimer arrangements on a quadratic lattice”, Physica, 27:12 (1961), 1209–1225 | DOI | Zbl

[6] Fisher M. E., “Statistical mechanics of dimers on a plane lattice”, Phys. Rev., 124:6 (1961), 1664–1672 | DOI | MR | Zbl

[7] Rushbrooke G. S., Scoins H. I., Wakefield A. J., “The vapour pressures of athermal mixtures”, Discuss. Farad. Soc., 1953, no. 15, 57–65 | DOI

[8] Trevena D. H., “The entropy of mixing of athermal monomer-dimer liquid mixtures”, Proc. Phys. Soc., 84:542 (1964), 969–974 | DOI | MR

[9] Nagle J. F., “New series-expansion method for the dimer problem”, Phys. Rev., 152:1 (1966), 190–197 | DOI

[10] Gaunt D. S., “Exact series-expansion study of the monomer-dimer problem”, Phys. Rev., 179:1 (1969), 174–186 | DOI

[11] Baxter R. J., “Dimers on a rectangular lattice”, J. Math. Phys., 9:4 (1968), 650–654 | DOI | MR

[12] Runnels L. K., “Exact finite method of lattice statistics. III: Dimers on the square lattice”, J. Math. Phys., 11:3 (1970), 842–850 | DOI

[13] Degrève L., “Expansion series for the dimer-monomer problem”, Physica, 66:2 (1973), 395–402 | DOI

[14] Van Craen J., Bellemans A., “The excess combinatorial entropy of monomer-dimer mixtures”, Bull. Acad. Pol. Sci. Ser. Sci. Chim., 19:1 (1971), 45–47

[15] Kaye R. D., Burley D. M., “Square lattice calculations for the general dimer and trimer problem using the Kikuchi method”, Physica, 87A:3 (1977), 499–514 | DOI

[16] Shulepov Yu. V., Aksenenko E. V., Reshetochnyi gaz, Naukova dumka, Kiev, 1981

[17] Percus J. K., Yevick G. J., “Analysis of classical statistical mechanics by means of collective coordinates”, Phys. Rev., 110:1 (1958), 1–8 | DOI | MR

[18] Percus J. K., “Approximation methods in classical statistical mechanics”, Phys. Rev. Lett., 8:11 (1962), 462–464 | DOI

[19] Wertheim M. S., “Integral equations in the theory of classical fluids”, J. Math. Phys., 8:4 (1967), 927–934 | DOI

[20] Shulepov Yu. V., “K statisticheskoi teorii neodnorodnykh klassicheskikh zhidkostei”, UFZh, 19:7 (1974), 1080–1085

[21] Verlet L., “On the theory of classical fluids, III”, Physica, 30:1 (1964), 95–104 | DOI | MR

[22] Rashbruk Dzh., “Ravnovesnye teorii zhidkogo sostoyaniya”, Fizika prostykh zhidkostei, Sb., ed. Zubarev D. N., Mir, M., 1971, 30–62

[23] Levesque D., Verlet L., “Integral equation for classical fluids and the lattice gas”, Phys. Lett., 11:1 (1964), 36–37 | DOI | MR

[24] Jancovici B., “Theory of freezing”, Physica, 31:7 (1965), 1017–1028 | DOI

[25] Heilmann O. J., Lieb E. H., “Theory of monomer-dimer systems”, Commun. Math. Phys., 25:3 (1972), 190–232 | DOI | MR | Zbl

[26] Gruber C., Kunz H., “General properties of polymer systems”, Commun. Math. Phys., 22:2 (1971), 133–161 | DOI | MR