Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

European Physical Journal B

Volumn 26, Issue 4, 2002, Pages 439-447

  Canals, B ^a   Garanin, D A ^b  

^a LABORATOIRE DE CRISTALLOGRAPHIE   (France)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

75.10.Hk Classical spin models; 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.); 75.50.Ee Antiferromagnetics

Indexed keywords

EID: 0041694477     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10051-002-8986-0     Document Type: Article

References (42)

1. For a collection of articles, see Magnetic systems with Competing Interactions: Frustated Spin System, edited by H.T. Diep (World Scientific, Singapore, 1994); for Ising systems, see R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, Berlin, 1986); for reviews, see A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994); P. Schiffer, A.P. Ramirez, Comments Cond. Mat. Phys. 18, 21 (1996); M.J. Harris, M.P. Zinkin, Mod. Phys. Lett. B 10, 417 (1996).
2. For a collection of articles, see Magnetic systems with Competing Interactions: Frustated Spin System, edited by H.T. Diep (World Scientific, Singapore, 1994); for Ising systems, see R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, Berlin, 1986); for reviews, see A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994); P. Schiffer, A.P. Ramirez, Comments Cond. Mat. Phys. 18, 21 (1996); M.J. Harris, M.P. Zinkin, Mod. Phys. Lett. B 10, 417 (1996).
3. For a collection of articles, see Magnetic systems with Competing Interactions: Frustated Spin System, edited by H.T. Diep (World Scientific, Singapore, 1994); for Ising systems, see R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, Berlin, 1986); for reviews, see A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994); P. Schiffer, A.P. Ramirez, Comments Cond. Mat. Phys. 18, 21 (1996); M.J. Harris, M.P. Zinkin, Mod. Phys. Lett. B 10, 417 (1996).
4. For a collection of articles, see Magnetic systems with Competing Interactions: Frustated Spin System, edited by H.T. Diep (World Scientific, Singapore, 1994); for Ising systems, see R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, Berlin, 1986); for reviews, see A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994); P. Schiffer, A.P. Ramirez, Comments Cond. Mat. Phys. 18, 21 (1996); M.J. Harris, M.P. Zinkin, Mod. Phys. Lett. B 10, 417 (1996).
5. For a collection of articles, see Magnetic systems with Competing Interactions: Frustated Spin System, edited by H.T. Diep (World Scientific, Singapore, 1994); for Ising systems, see R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, Berlin, 1986); for reviews, see A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994); P. Schiffer, A.P. Ramirez, Comments Cond. Mat. Phys. 18, 21 (1996); M.J. Harris, M.P. Zinkin, Mod. Phys. Lett. B 10, 417 (1996).
6. G.H. Wannier, Phys. Rev. 79, 357 (1950).
7. E.H. Lieb, P. Schupp, Phys. Rev. Lett. 83, 5362 (1999).
8. B. Canals, to be published in Phys. Rev. B.
9. R. Moessner, O. Tchernyshyov, S.L. Sondhi, cond-mat/0106286.
10. J.-B. Fouet, M. Mambrini, P. Sindzingre, C. Lhuillier, to be published in Phys. Rev. B.
11. M. Elhajal, B. Canals, C. Lacroix, Can. J. Phys. 79, 1353 (2001).
12. H.E. Stanley, Phys. Rev. Lett. 20, 589 (1968).
13. H.E. Stanley, in Phase Transitions and Critical Phenomena, edited by C. Domb, M.S. Green (Academic Press, New York, 1974), Vol. 3.
14. H.E. Stanley, Phys. Rev. 176, 718 (1968).
15. T.N. Berlin, M. Kac, Phys. Rev. 86, 821 (1952).
16. G.S. Joyce, in Phase Transitions and Critical Phenomena, edited by C. Domb, M.S. Green (Academic Press, New York, 1972), Vol. 2.
17. A. Auerbach, D.P. Arovas, Phys. Rev. Lett. 61,617(1988); , Phys. Rev. B 38, 326 (1988).
18. A. Auerbach, D.P. Arovas, Phys. Rev. Lett. 61,617(1988); , Phys. Rev. B 38, 326 (1988).
19. S. Sachdev, Phys. Rev. B 45, 12377 (1992).
20. C. Timm, S.M. Girvin, P. Henelius, Phys. Rev. B 58, 1464 (1998).
21. S. Chakravarty, B.I. Halperin, D.R. Nelson, Phys. Rev. Lett. 60, 1057 (1988); Phys. Rev. B 39, 2344 (1989).
22. S. Chakravarty, B.I. Halperin, D.R. Nelson, Phys. Rev. Lett. 60, 1057 (1988); Phys. Rev. B 39, 2344 (1989).
23. A.V. Chubukov, S. Sachdev, J. Ye, Phys. Rev. B 49, 11919 (1994).
24. A.V. Chubukov, O.A. Starykh, Phys. Rev. B 53, R14729-R14732 (1996).
25. S. Ma, Modern Theory of Critical Phenomena (Benjamin, New York, 1973).
26. R. Abe, Prog. Theor. Phys. 48, 1414 (1972); 49, 113 (1973).
27. R. Abe, Prog. Theor. Phys. 48, 1414 (1972); 49, 113 (1973).
28. R. Abe, S. Hikami, Prog. Theor. Phys. 49, 442 (1973); 57, 1197 (1977).
29. R. Abe, S. Hikami, Prog. Theor. Phys. 49, 442 (1973); 57, 1197 (1977).
30. Y. Okabe, M. Masutani, Phys. Lett. A 65, 97 (1978).
31. B. Canals, D.A. Garanin, Can. J. Phys. 79, 1323 (2001).
32. The calculations for a four sites unit cell have been done but we choose to report a two sites description for simplicity. The reader is referred to previous work if necessary [23].
33. D.A. Garanin, J. Stat. Phys. 74, 275 (1994).
34. D.A. Garanin, V.S. Lutovinov, Solid State Commun. 50, 219 (1984).
35. D.A. Garanin, Phys. Rev. B 53, 11593 (1996).
36. D.A. Garanin, B. Canals, Phys. Rev. B 59, 443 (1999).
37. D.A. Garanin, J. Stat. Phys. 83, 907 (1996).
38. J.N. Reimers, Phys. Rev. B 46, 193 (1992).
39. J.N. Reimers, Phys. Rev. B 45, 7287 (1992).
40. R. Moessner, A.J. Berlinsky, Phys. Rev. Lett. 83, 3293 (1999).
41. Authors have integrated exactly the partition function as well as the susceptibility of a tetrahedron which also corresponds in our case to the four sites unit cell of the checkerboard lattice when described as a square lattice of tetrahedra.
42. J.T. Chalker, P.C.W. Holdsworth, E.F. Shender, Phys. Rev. Lett. 68, 855 (1992).