Classical dimers with aligning interactions on the square lattice

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

Volumn 74, Issue 4, 2006, Pages

  Alet, Fabien ^a,b   Ikhlef, Yacine ^b,c   Jacobsen, Jesper Lykke ^b,c   Misguich, Grégoire ^b   Pasquier, Vincent ^b  

^a CNRS   (France)

^b CEA SACLAY   (France)

^c UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; MAPPING; MATHEMATICAL MODELS; MONOMERS; MONTE CARLO METHODS; PHASE TRANSITIONS;

BETHE ANSATZ; COUPLING CONSTANT; KOSTERLITZ THOULESS PHASE TRANSITION;

DIMERS;

EID: 33750469338     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.041124     Document Type: Article

References (68)

1. J. K. Roberts, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 152, 464 (1935);
2. R. H. Fowler and G. S. Rushbrooke, Trans. Faraday Soc. TFSOA4 0014-7672 10.1039/tf9373301272 33, 1272 (1937).
3. P. W. Kasteleyn, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/0031-8914(61)90063-5 27, 1209 (1961);
4. H. N. V. Temperley and M. E. Fisher, Philos. Mag. PHMAA4 0031-8086 6, 1061 (1961).
5. M. E. Fisher, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.124.1664 124, 1664 (1961).
6. M. E. Fisher and J. Stephenson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.132.1411 132, 1411 (1963).
7. R. Kenyon, math.CO/0310326, and references therein.
8. H. W. J. Blöte and H. J. Hilhorst, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/15/11/011 15, L631 (1982);
9. B. Nienhuis, H. J. Hilhorst, and H. W. J. Blöte, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/18/025 17, 3559 (1984).
10. D. Huse, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.167004 91, 167004 (2003).
11. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.2376 61, 2376 (1988).
12. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1881 86, 1881 (2001);
13. G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.137202 89, 137202 (2002);
14. R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.024504 65, 024504 (2002);
15. D. A. Ivanov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.094430 70, 094430 (2004).
16. J. M. Kosterlitz and D. J. Thouless, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/6/7/010 6, 1181 (1973);
17. V. L. Berezinskii, Sov. Phys. JETP SPHJAR 0038-5646 32, 493 (1971).
18. B. Nienhuis, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic, London, 1987), Vol. 11.
19. F. Alet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.235702 94, 235702 (2005).
20. O. J. Hellmann and E. Præstgaard, Chem. Phys. CMPHC2 0301-0104 10.1016/0301-0104(77)85085-4 24, 119 (1977);
21. D. Poland and P. K. Swaminathan, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.438547 71, 1926 (1979).
22. J. G. Brankov, V. B. Velichkov, and V. B. Priezzhev, J. Mol. Liq. JMLIDT 0167-7322 53, 15 (1992);
23. J. G. Brandkov and R. A. Karamikhova, Physica A PHYADX 0378-4371 162, 298 (1990).
24. C. Castelnovo, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.144411 73, 144411 (2006);
25. C. Castelnovo, e-print cond-mat/0602237.
26. D. Poilblanc, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.014437 74, 014437 (2006).
27. S. Papanikolaou, E. Luijten, and E. Fradkin, e-print cond-mat/0607316.
28. F. Alet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.030403 97, 030403 (2006).
29. A. W. Sandvik and R. Moessner, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.144504 73, 144504 (2006)
30. O. F. Syljuåsen and A. W. Sandvik, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046701 66, 046701 (2002).
31. F. Alet and E. S. Sørensen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.026702 68, 026702 (2003).
32. J. L. Cardy, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/7/003 17, L385 (1984).
33. 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);
34. I. Affleck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.746 56, 746 (1986).
35. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford University Press, Oxford, 1988).
36. P. W. Leung, K. C. Chiu, and K. J. Runge, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.12938 54, 12938 (1996).
37. S. Sachdev, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.5204 40, 5204 (1989).
38. K. Binder, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01293604 43, 119 (1981).
39. M. S. S. Challa, D. P. Landau, and K. Binder, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.1841 34, 1841 (1986).
40. W. Krauth and R. Moessner, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.064503 67, 064503 (2003).
41. The four corners in fact have the same height.
42. J. Kondev and C. L. Henley, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.6628 52, 6628 (1995);
43. J. Kondev and C. L. Henley, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(96)00064-8 464, 540 (1996);
44. C. Zeng and C. L. Henley, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.14935 55, 14935 (1997);
45. R. Raghavan, C. L. Henley, and S. L. Arouh, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02199112 86, 517 (1997).
46. S. Coleman, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.11.2088 11, 2088 (1975).
47. g is related to the stiffness constant K used in Ref. by g=8Kπ.
48. By exponent, we denote the actual exponent of a charge-charge correlation function, not the scaling dimension X(e,m) of the electromagnetic operator. We have the simple relation α(e,m)=2X(e,m).
49. E. Fradkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.224415 69, 224415 (2004).
50. M. Levin and T. Senthil, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.220403 70, 220403 (2004).
51. J. Ashkin and E. Teller, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.64. 178 64, 178 (1943).
52. R. J. Baxter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.26. 832 26, 832 (1971);
53. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982).
54. B. Nienhuis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.43.737 43, 737 (1979).
55. If monomers (magnetic charges) were allowed, the flux would count the number of monomers on the even sublattice (magnetic charge +1) minus the number of monomers on the odd sublattice (charge -1).
56. S. K. Yang, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(87)90334-8 285, 183 (1987);
57. P. Di Francesco, H. Saleur, and J.-B. Zuber, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01009954 49, 57 (1987).
58. C. Boutillier and B. de Tilière, math.PR/0608600.
59. A. Luther and I. Peschel, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.12.3908 12, 3908 (1975).
60. O. F. Syljuåsen, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S021797920502964X 19, 1973 (2005).
61. O. F. Syljuåsen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71. 020401 71, 020401 (R) (2005).
62. O. F. Syljuåsen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73. 245105 73, 245105 (2006).
63. The MC simulations are difficult in this case, and for t→ a transition happening only at T=0 cannot be excluded. This would reduce the occupation of the phase diagram by the staggered phase to a simple T=0 line.
64. A. Ralko, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.224109 71, 224109 (2005).
65. F. Alet, J. Phys. Soc. Jpn. Suppl. JUPSAU 0031-9015 74, 30 (2005);
66. M. Troyer, B. Ammon, and E. Heeb, Lect. Notes Comput. Sci. LNCSD9 0302-9743 1505, 191 (1998); see http://alps.comp-phys.org
67. L. Levitov, see http://www.mit.edu/~levitov/8.334/
68. A. M. Polyakov, Gauge Fields and Strings (Harwood, Amsterdam, 1987).