Bond-propagation algorithm for thermodynamic functions in general two-dimensional Ising models

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 1, 2007, Pages

  Loh, Y L ^a   Carlson, E W ^a   Tan, M Y J ^b  

^a PURDUE UNIVERSITY   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34447125112     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.014404     Document Type: Article

References (29)

1. H. Nishimori, Statistical Physics of Spin Glasses and Information Processing (Oxford University Press, Oxford, 2001).
2. Y. L. Loh and E. W. Carlson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.227205 97, 227205 (2006).
3. F. Merz and J. T. Chalker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.054425 65, 054425 (2002).
4. P. W. Kasteleyn, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703953 4, 287 (1963).
5. M. E. Fisher, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704796 7, 10 (1966).
6. L. Saul and M. Kardar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48. R3221 48, R3221 (1993).
7. L. Saul and M. Kardar, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90037-X 432, 641 (1994).
8. A. Galluccio, M. Loebl, and J. Vondrak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5924 84, 5924 (2000).
9. R. M. F. Houtappel, Physica PHYSAG 0031-8914 10.1016/0031-8914(50)90130-3 16, 425 (1950).
10. I. Syozi, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M. S. Green, (Academic, New York, 1972), Vol. 1.
11. C. J. Colbourn, J. S. Provan, and D. Vertigan, Discrete Appl. Math. DAMADU 0166-218X 10.1016/0166-218X(95)E0111-3 60, 119 (1995).
12. T. A. Feo and J. S. Provan, Oper. Res. OPREAI 0030-364X 41, 572 (1993).
13. D. J. Frank and C. J. Lobb, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.37.302 37, 302 (1988).
14. D. Archdeacon, C. J. Colbourn, I. Gitler, and J. S. Provan, J. Graph Theory JGTHDO 0364-9024 10.1002/(SICI)1097-0118(200002)33:2<83::AID- JGT3>3.0.CO;2-P 33, 83 (2000).
15. B. Derrida and L. de Seze, J. Phys. (Paris) JOPQAG 0302-0738 43, 475 (1982).
16. B. Derrida and J. Vannimenus, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/15/10/007 15, L557 (1982).
17. K. Truemper, J. Graph Theory JGTHDO 0364-9024 10.1002/jgt.3190130202 13, 141 (1989).
18. I. Gitler, Ph.D. thesis, University of Waterloo, 1991.
19. I. Gitler, report, 1991 (unpublished).
20. H. J. Hilhorst, M. Schick, and J. M. J. van Leeuwen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.40.1605 40, 1605 (1978).
21. H. J. Hilhorst, M. Schick, and J. M. J. van Leeuwen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.19.2749 19, 2749 (1979).
22. A. George, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. SJNAEQ 0036-1429 10.1137/0710032 10, 345 (1973).
23. R. J. Lipton, D. Rose, and R. E. Tarjan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. SJNAEQ 0036-1429 10.1137/0716027 16, 346 (1979).
24. I. Morgenstern and K. Binder, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.43.1615 43, 1615 (1979).
25. N. Robertson and P. D. Seymour, J. Comb. Theory, Ser. B JCBTB8 0095-8956 10.1016/j.jctb.2004.08.001 92, 325 (2004).
26. M. Mancini and C. Oguey, Eur. Phys. J. E EPJSFH 1292-8941 10.1140/epje/e2007-00024-y 22, 181 (2007).
27. A. Lehman, J. Soc. Ind. Appl. Math. JSIMAV 0368-4245 10.1137/0111058 11, 773 (1963).
28. G. Odor, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.663 76, 663 (2004).
29. J. H. H. Perk and H. Au-Yang, Encyclopedia of Mathematical Physics, edited by, J.-P. Françoise,,, G. L. Naber,, and, S. T. Tsou, (Oxford: Elsevier, 2006), Vol. 5, pp. 465-473.