Classical dimers on the triangular lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 21, 2002, Pages 2145131-21451314

  Fendley, P ^a   Moessner, R ^b   Sondhi, S L ^c  

^a University of Virginia   (United States)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; CORRELATION FUNCTION; DIMERIZATION; ELECTRIC CONDUCTIVITY; ENTROPY; MODEL; QUANTUM MECHANICS; SOLID PHASE EXTRACTION; STATISTICAL ANALYSIS; THERMODYNAMICS;

EID: 0036978398     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. P. W. Kasteleyn, Physica (Amsterdam) 27, 1209 (1961); J. Math. Phys. 4, 287 (1963).
2. P. W. Kasteleyn, Physica (Amsterdam) 27, 1209 (1961); J. Math. Phys. 4, 287 (1963).
3. M. E. Fisher, J. Math. Phys. 7, 1776 (1966).
4. J. F. Nagle, C. S. O. Yokio, and S. M. Bhattacharjee, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic-Press, New York, 1980), Vol. 13.
5. M. E. Fisher and J. Stephenson, Phys. Rev. 132, 1411 (1963).
6. B. M. McCoy and T. T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, MA, 1973).
7. P. W. Anderson, Science 235, 1196 (1987).
8. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
9. The precise connection between classical and quantum correlations requires additional assumptions about the ergodicity of the quantum dimer Hamiltonian in the space of dimer configurations (Refs. 7 and 9). This problem was addressed for a finite triangular lattice with open boundary conditions in C. Kenyon and E. Remila, Discrete Math. 152, 191 (1996).
10. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001).
11. F. Y. Wu, Phys. Rev. 168, 539 (1967).
12. X. G. Wen, Phys. Rev. B 40, 7387 (1989); Int. J. Mod. Phys. B 4, 239 (1990); X. G. Wen and Q. Niu, Phys. Rev. B 41, 9377 (1990).
13. X. G. Wen, Phys. Rev. B 40, 7387 (1989); Int. J. Mod. Phys. B 4, 239 (1990); X. G. Wen and Q. Niu, Phys. Rev. B 41, 9377 (1990).
14. X. G. Wen, Phys. Rev. B 40, 7387 (1989); Int. J. Mod. Phys. B 4, 239 (1990); X. G. Wen and Q. Niu, Phys. Rev. B 41, 9377 (1990).
15. R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B 65, 024504 (2002).
16. J. F. Nagle, Phys. Rev. 152, 190 (1966).
17. D. S. Gaunt, Phys. Rev. 179, 174 (1969).
18. S. Samuel, J. Math. Phys. 21, 2806 (1980).
19. F. Mila, Phys. Rev. Lett. 81, 2356 (1998).
20. W. F. Wolff and J. Zittartz, Z. Phys. B: Condens. Matter B49, 139 (1982).
21. An actual magnetic model will exhibit a finite density of spinons as a finite temperature. Our diagnostic is the equivalent of the "Polyakov loop" for gauge theories without dynamical matter, at finite temperatures. The latter measures the free energy of two static quarks at varying separations.
22. This problem was concurrently studied numerically (by Monte Carlo simulations and by exact enumeration) by W. Krauth and R. Moessner, cond-mat/0206177 (unpublished).
23. M. E. Fisher, Phys. Rev. 124, 1664 (1961).
24. M. E. Fisher and H. N. V. Temperley, Philos. Mag. 6, 1061 (1961).
25. The corresponding expression for g in Ref. 9 contains an error in the sign of the argument of the first exponential, which is corrected here.
26. R. E. Hartwig, J. Math. Phys. 7, 286 (1966).
27. R. Moessner and S. L. Sondhi, Phys. Rev. B 62, 14 122 (2000).
28. H. Au-Yang and J. H. H. Perk, Phys. Lett. A 104, 131 (1984).
29. N. Read and B. Chakraborty, Phys. Rev. B 40, 7133 (1989).
30. S. Kivelson, Phys. Rev. B 39, 259 (1989).
31. L. Balents, M. P. A. Fisher, and S. M. Girvin, Phys. Rev. B 65, 224412 (2002).
32. K. Shtengel (private communication).
33. G. Forgacs, Phys. Rev. B 22, 4473 (1980).
34. R. Moessner and S. L. Sondhi (unpublished).
35. E. H. Fradkin and S. H. Shenker, Phys. Rev. D 19, 3682 (1979).
36. A. Erdelyi, Bateman Manuscript Project: Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. 2.
37. E. T. Whitaker and G. N. Watson, A Course in Modern Analysis (Cambridge University Press, Cambridge, 1927).
38. We thank Michael Fowler for providing this proof.