Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field

Physica A: Statistical Mechanics and its Applications

Volumn 289, Issue 1-2, 2001, Pages 137-156

  Dixon, J M ^a   Tuszynski, J A ^b   Nip, M L A ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MAGNETIC FIELDS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA;

ISING HAMILTONIAN;

PHASE TRANSITIONS;

EID: 0035153344     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(00)00318-6     Document Type: Article

References (26)

1. A.D. Bruce, R.A. Cowley, Structural Phase Transitions, Taylor & Francis, London, 1981.
2. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Clarendon Press, Oxford, 1971.
3. G.D. Mahan, W.L. Roth (Eds.), Superionic Conductors, Plenum Press, New York, 1976.
4. A. Bienenstock, J. Lewis, Phys. Rev. 160 (1967) 393.
5. R.J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, New York, 1982.
6. K. Huang, Statistical Mechanics, Wiley, New York, 1987.
7. L. Onsager, Phys. Rev. 65 (1944) 117.
8. N.D. Mermin, H. Wagner, Phys. Rev. Lett. A 17 (1966) 1133.
9. T.H. Berlin, M. Kac, Phys. Rev. 86 (1952) 821.
10. H.E. Stanley, Phys. Rev. 176 (1968) 718.
11. F.Y. Wu, Rev. Mod. Phys. 54 (1982) 235.
12. H.A. Kramers, G.H. Wannier, Phys. Rev. 60 (1941) 252.
13. R. Kubo, Busseiron Kenkyu 1 (1943) 1.
14. J.C. Bonner, G. Müller, Phys. Rev. B 29 (9) (1984) 5216-5221.
15. J.C. Bonner, M.E. Fisher, Phys. Rev. A 135 (1964) 640.
16. G.A. Baker Jr., G.S. Rushbrooke, H.E. Gilbert, Phys. Rev. A 135 (1964) 1272.
17. J. Kondo, K. Yamaji, Prog. Theor. Phys. 47 (1972) 807.
18. J.J. Cullen, D.P. Landau, Phys. Rev. B 27 (1983) 297.
19. J.W. Lyklema, Phys. Rev. B 27 (1983) 3108.
20. M. Marcu, J. Müller, K.F. Schmatzer, J. Phys. A 18 (1985) 3189.
21. P. Schlottmann, Phys. Rev. B 33 (1986) 4880.
22. M. Takahashi, M. Yamada, J. Phys. Soc. Japan 55 (1986) 2024.
23. C.K. Majumdar, I. Ramarao, Phys. Rev. B 22 (7) (1980) 3288-3293.
24. J.M. Dixon, R.S. Wardlaw, J. Phys. C 19 (1986) 943-961.
25. E. Fradkin, Field Theories of Condensed Matter Systems, Addison-Wesley, Redwood City, 1991.
26. J.M. Yeomans, Statistical Mechanics of Phase Transitions, Oxford University Press, Oxford, 1992.