Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 1, 2006, Pages

  Kong, Yong ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; DIMERS; FREE ENERGY; MATHEMATICAL MODELS;

FREE ENERGY PER LATTICE SITE; LATTICE OF DIMERS; LOGARITHMIC CORRECTION; MONOMER-DIMER MODEL;

MONOMERS;

EID: 33746103694     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.011102     Document Type: Article

References (34)

1. P. W. Kasteleyn, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/0031-8914(61)90063-5 27, 1209 (1961);
2. H. N. V. Temperley and M. E. Fisher, Philos. Mag. PHMAA4 0031-8086 6, 1061 (1961);
3. M. E. Fisher, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.124.1664 124, 1664 (1961).
4. J. F. Nagle, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.152.190 152, 190 (1966);
5. D. Gaunt, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.179.174 179, 174 (1969).
6. J. Bondy and D. Welsh, Proc. R. Soc., Math. Physic. Eng. Sci. ZZZZZZ 1364-5021 62, 503 (1966);
7. J. Hammersley, Proc. R. Soc., Math. Physic. Eng. Sci. ZZZZZZ 1364-5021 64, 455 (1968);
8. J. Hammersley and V. Menon, J. Inst. Math. Appl. JMTAA8 0020-2932 6, 341 (1970).
9. M. E. Fisher and J. Stephenson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.132.1411 132, 1411 (1963);
10. R. E. Hartwig, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704931 7, 286 (1966).
11. O. J. Heilmann and E. H. Lieb, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01877590 25, 190 (1972);
12. C. Gruber and H. Kunz, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01651334 22, 133 (1971).
13. C. Kenyon, D. Randall, and A. Sinclair, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02183743 83, 637 (1996).
14. W.-J. Tzeng and F. Y. Wu, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1022155701655 110, 671 (2003).
15. P. W. Kasteleyn, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703953 4, 287 (1963);
16. M. E. Fisher, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704825 7, 1776 (1966).
17. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.2376 61, 2376 (1988);
18. F. Alet, J. L. Jacobsen, G. Misguich, V. Pasquier, F. Mila, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.235702 94, 235702 (2005).
19. M. Jerrum, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01010403 48, 121 (1987);
20. M. Jerrum, J. Stat. Phys. JSTPBS 0022-4715 59, 1087(E) (1990).
21. M. R. Garey and D. S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness (W. H. Freeman and Company, New York, 1979).
22. D. J. A. Welsh, Complexity: Knots, Colourings, and Counting, Vol. 186 of London Mathematical Society Lecture Note Series (Cambridge University Press, Cambridge, 1993).
23. H. W. J. Blöte, J. L. Cardy, and M. P. Nightingale, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.742 56, 742 (1986);
24. I. Affleck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.746 56, 746 (1986).
25. J. L. Cardy and I. Peschel, Nucl. Phys. NUPBBO 0550-3213 300[FS22], 377 (1988);
26. V. Privman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.9261 38, 9261 (1988).
27. J. G. Brankov, J. Math. Phys. JMAPAQ 0022-2488 36, 5071 (1995).
28. N. S. Izmailian, V. B. Priezzhev, P. Ruelle, and C.-K. Hu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.260602 95, 260602 (2005).
29. A. E. Ferdinand, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1705162 8, 2332 (1967).
30. C. Itzykson, H. Saleur, and J.-B. Zuber, Europhys. Lett. EULEEJ 0295-5075 2, 91 (1986).
31. Y. Kong, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.016106 73, 016106 (2006).
32. Y. Kong, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.479242 111, 4790 (1999).
33. P. E. John and H. Sachs, Discrete Math. DSMHA4 0012-365X 10.1016/S0012-365X(99)00301-5 216, 211 (2000).
34. H. N. V. Temperley, in Combinatorics: Proceedings of the British Combinatorial Conference 1973 Vol. 13 of London Mathematical Society Lecture Note Series, (Cambridge University Press, Cambridge, England, 1974), pp. 202-204.