Intersecting loop models on ℤd: Rigorous results

Nuclear Physics B

Volumn 570, Issue 3, 2000, Pages 590-614

  Chayes, L ^a   Pryadko, Leonid P ^b   Shtengel, Kirill ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Loop models; Phase transitions; Reflection positivity

Indexed keywords

EID: 0034719556     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00780-4     Document Type: Article

References (27)

1. J. Kondev, Int. J. Mod. Phys. B 11 (1997) 153, cond-mat/9607181.
2. S.O. Warnaar, B. Nienhuis, J. Phys. A: Math. Gen. 26 (1993) 2301.
3. H.A. Kramers, G.H. Wannier, Phys. Rev. 60 (1941) 252.
4. M. Kac, J.C. Ward, Phys. Rev. 88 (1952) 1332.
5. N.V. Vdovichenko, Sov. Phys. JETP 20 (1965) 477.
6. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982).
7. E. Domany et al., Nucl. Phys. 190 (1981) 279.
8. B. Nienhuis, Phys. Rev. Lett. 49 (1982) 1062.
9. B. Nienhuis, Int. J. Mod. Phys. B 4 (1990) 929.
10. H.W.J. Blöte, B. Nienhuis, J. Phys. A: Math. Gen. 22 (1989) 1415.
11. M.T. Batchelor, B. Nienhuis, S.O. Warnaar, Phys. Rev. Lett. 62 (1989) 2425.
12. M. Aizenman, B. Nachtergaele, Commun. Math. Phys. 164 (1994) 17.
13. M.J. Martins, B. Nienhuis, R. Rietman, Phys. Rev. Lett. 81 (1997) 504, cond-mat/9709051.
14. R.J. Baxter, J. Phys. A: Math. Gen. 19 (1986) 2821.
15. J. Kondev, C.L. Henley, Phys. Rev. B 52 (1995) 6628.
16. J.L. Jacobsen, J. Kondev, Nuclear Physics B 532 (1998) 635, cond-mat/9804048.
17. J.L. Jacobsen, J. Kondev, J. Stat. Phys. 96 (1999) 21, cond-mat/9811085.
18. J.V. Jose et al., Phys. Rev. B 16 (1977) 1217.
19. H.J.F. Knops, Phys. Rev. Lett. 39 (1977) 766.
20. J. Ashkin, E. Teller, Phys. Rev. 64 (1943) 178.
21. D.B. Abraham, C.M. Newman, Phys. Rev. Lett. 61 (1988) 1969.
22. L. Chayes, J. Machta, Physica A 239 (1997) 542.
23. C.E. Pfister, Y. Velenik, J. Stat. Phys. 88 (1997) 1295, cond-mat/9704017.
24. L. Chayes, K. Shtengel, Commun. Math. Phys. 204 (1999) 353, cond-mat/9811203.
25. T. Baker, L. Chayes, J. Stat. Phys. 93 (1998) 1.
26. S.B. Shlosman, Russ. Math. Surv. 41:3 (1986) 83.
27. N. Madras, G. Slade, The Self-avoiding Walk (Birkhäuser, Boston, 1993).