The Onsager Formula

Yu. M. Zinoviev

Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 298-319.

Résumé

The Onsager formula for the statistical sum of the two-dimensional Ising model with periodic boundary conditions is proved.

Bibliographie

[1] Onsager L., “Crystal statistics. I: A two-dimensional model with an order–disorder transition”, Phys. Rev., 65:3–4 (1944), 117–149 | DOI | MR | Zbl

[2] Kaufman B., “Crystal statistics. II: Partition function evalueted by spinor analysis”, Phys. Rev., 74:6 (1949), 1232–1243 | DOI

[3] Kaufman B., Onsager L., “Crystal statistics. III: Short-range order in a binary Ising lattice”, Phys. Rev., 74:6 (1949), 1244–1252 | DOI

[4] Kac M., Ward J. C., “A combinatorial solution of the two-dimensional Ising model”, Phys. Rev., 88:6 (1952), 1332–1337 | DOI | Zbl

[5] Sherman S., “Combinatorial aspects of the Ising model for ferromagnetism. I: A conjecture of Feynman on paths and graphs”, J. Math. Phys., 1:3 (1960), 202–217 | DOI | MR

[6] Hurst C. A., Green H. S., “New solution of the Ising problem for a rectangular lattice”, J. Chem. Phys., 33:4 (1960), 1059–1062 | DOI | MR

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

[8] Fisher M. E., “On the dimer solution of planar Ising model”, J. Math. Phys., 7:10 (1966), 1776–1781 | DOI

[9] McCoy B. M., Tai Tsun Wu., The two-dimensional Ising model, Harvard Univ. Press, Cambridge, MA, 1973

[10] Dolbilin N. P., Zinovev Yu. M., Mischenko A. S., Shtanko M. A., Shtogrin M. I., “Gomologicheskie svoistva dimernykh pokrytii reshetok na poverkhnostyakh”, Funkts. analiz i ego pril., 30:3 (1996), 19–33 | MR | Zbl

[11] Van der Waerden B. L., “Lange Reichweite der regelmassigen Atomanordnung in Mischkristallen”, Ztsch. Phys., 118:2 (1941), 473–488

[12] Burbaki N., Algebra. Moduli, koltsa, formy, Nauka, M., 1966 | MR