Thermodynamic functions of three-dimensional ising model near the phase transition point with allowance for corrections to scaling. I. The case $T>T_c$

M. P. Kozlovskii   ; I. V. Pylyuk   ; I. R. Yukhnovskii

Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 2, pp. 293-316

Résumé

A method is proposed for finding explicit expressions for the thermodynamic functions of the three-dimensional Ising model at $T>T_c$ with allowance for confluent corrections. The critical exponents are found together with expressions for the critical amplitudes of the basic characteristics of the model (free energy, entropy, internal energy, specific heat, susceptibility) as functions of the microscopic parameters of the Hamiltonian. It is shown that positivity and correct temperature dependence of the entropy and specific heat are ensured by the contribution of the long-wavelength phases of the fluctuations of the spin-moment density. The short-wavelength phases are responsible for the formation of the values of the critical exponents.

Bibliographie

[1] Zubarev D. N., ZhETF, 25:5 (1953), 548–559

[2] Yukhnovskii I. R., Fazovye perekhody vtorogo roda. Metod kollektivnykh peremennykh, Naukova dumka, Kiev, 1985 | MR

[3] Barmatz M., Hohenberg P. C., Kornblitt A., Phys. Rev., B12:5 (1975), 1947–1968 | DOI

[4] Jensen S. J. K., Mouritsen O. G., J. Phys. A, 15:8 (1982), 2631–2636 | DOI | MR

[5] Le Guillou J. C., Zinn-Justin J., Phys. Rev., B21:9 (1980), 3976–3998 | DOI | Zbl

[6] Yukhnovs'kii I. R., Rivista del Nuovo Cimento, 12:1 (1989), 1–120 | DOI | MR

[7] Kozlovsky M. P., Pylyuk I. V., Free energy and other thermodynamical functions above the second-order phase transition point, Preprint ITP-85-23E, ITP Acad. Sci. Ukr. SSR, Kiev, 1985

[8] Kozlovskii M. P., Pylyuk I. V., Raschet popravok k skeilingu v vyrazheniyakh dlya termodinamicheskikh funktsii modeli Izinga, Preprint ITF-89-24R, ITF AN USSR, Kiev, 1989

[9] Yukhnovskii I. R., TMF, 36:3 (1978), 373–399

[10] Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, eds. Abramovits M., Stigan I., Nauka, M., 1979 | MR

[11] Kozlovskii M. P., TMF, 78:3 (1989), 422–433 | MR

[12] Yukhnovskii I. R., Kozlovskii M. P., Kolomiets V. A., UFZh, 27:6 (1982), 925–930 | MR

[13] Ma Sh. K., Sovremennaya teoriya kriticheskikh yavlenii, Mir, M., 1980

[14] Yukhnovskii I. R., Kozlovskii M. P., Pylyuk I. V., Uchet popravki na usrednenie potentsiala v metode poetapnogo vychisleniya statsummy odnokomponentnoi spinovoi sistemy vblizi $T_c$, Preprint ITF-88-105R, ITF AN USSR, Kiev, 1988

[15] Yukhnovskii I. R., Kozlovskii M. P., Kolomiets V. A., UFZh, 27:9 (1982), 1399–1403 | MR

[16] Kozlovskii M. P., Fizika mnogochastich. sistem., no. 4, 1983, 37–44

[17] Kozlovskii M. P., Resheniya uravnenii renormgruppy dlya sistemy izingovskikh spinov v modeli $\rho^6$, Preprint ITF-84-35R, ITF AN USSR, Kiev, 1984

[18] Kozlovskii M. P., Pylyuk I. V., Raschet termodinamicheskikh funktsii vblizi tochki fazovogo perekhoda v priblizhenii shesternoi bazisnoi mery, Preprint ITF-87-9R, ITF AN USSR, Kiev, 1987

[19] Pylyuk I. V., Kozlovskii M. P., Issledovanie modeli Izinga s ispolzovaniem negaussovykh bazisnykh mer, Preprint ITF-87-31R, ITF AN USSR, Kiev, 1987

[20] Pylyuk I. V., Kriticheskoe povedenie trekhmernoi odnokomponentnoi spinovoi sistemy v metode kollektivnykh peremennykh pri uslozhnenii bazisnoi mery, Preprint ITF-88-107R, ITF AN USSR, Kiev, 1988

[21] Kozlovskii M. P., Oblast primenimosti renormgruppovykh sootnoshenii pri opisanii fazovogo perekhoda vtorogo roda. Trudy soveschaniya “Renormgruppa-86”, D2-87-123, OIYaI, Dubna, 1987, S. 300–314 | MR

[22] Liu A. J., Fisher M. E., Physica A, 156:1 (1989), 35–76 | DOI | MR

[23] Kadanoff L. P., Physica A, 163:1 (1990), 1–14 | DOI | MR