Geodesic
Ising model with magnetic field and the diophantine moment problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 1, pp. 3-15
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The properties of the Lee–Yang measure describing the distribution of the zeros of the partition function for the ferromagnetic Ising model with magnetic field that follow from the condition that its moments be Diophantine are studied. 
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V. S. Vladimirov; I. V. Volovich. Ising model with magnetic field and the diophantine moment problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/TMF_1982_53_1_a0/

[1] Yang C. N., Lee T. D., “Statistical theory of equations of state and phase transitions”, Phys. Rev., 87:3 (1952), 404–419 | DOI | MR

[2] Abe R., “Note on the critical behavior of Ising ferromagnets”, Progr. Theor. Phys., 38:1 (1967), 72–80 | DOI

[3] Suzuki M., “A theory of the second order phase transitions in spin systems. II: Complex magnetic field”, Progr. Theor. Phys., 38:6 (1967), 1225–1242 | DOI | MR

[4] Barnsley M., Bessis D., Moussa P., “The Diophantine moment problem and the analytic structure in the activity of the ferromagnetic Ising model”, J. Math. Phys., 20:4 (1979), 535–552 | DOI | MR

[5] Vladimirov V. S., “Diofantova problema momentov i model Izinga”, DAN SSSR, 264:6 (1982), 1301–1305 | MR | Zbl

[6] Helson H., “Note on harmonic functions”, Proc. Amer. Math. Soc., 4:5 (1953), 686–691 | DOI | MR | Zbl

[7] Nevanlinna R., Odnoznachnye analiticheskie funktsii, Gostekhizdat, Leningrad, 1941, 338 pp. | MR

[8] Griffiths R. B., “Correlations in Ising ferromagnets”, J. Math. Phys., 8:3 (1967), 478–489 | DOI

[9] Ito K. R., “Remarks on the relation between the Lee-Yang circle theorem and the correlation inequalities”, Commun. Math. Phys., 47:2 (1976), 143–154 | DOI | MR

[10] Yang C. N., “The spontaneous magnetization of a two-dimensional Ising Model”, Phys. Rev., 85 (1952), 808–816 | DOI | MR | Zbl

[11] N. N. Bogolyubov, Kvazisrednie v zadachakh statisticheskoi mekhaniki. Izbr. tr., t. 3, Naukova dumka, Kiev, 1970 | MR

[12] Loomis L. H., “The converse of the Fatou theorem for positive harmonic functions”, Trans. Amer. Math. Soc., 53:2 (1943), 239–250 | DOI | MR | Zbl

[13] Rudin U., Teoriya funktsii v polikruge, Mir, M., 1974 | MR | Zbl

[14] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[15] Grenander U., Sege G., Teplitsevy formy i ikh prilozheniya, IL, M., 1961 | MR