Phase transition in the three-state potts antiferromagnet on the diced lattice

Physical Review Letters

Volumn 101, Issue 3, 2008, Pages

  Kotecký, Roman ^a,b   Salas, Jesús ^c   Sokal, Alan D ^d,e  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^d POLYTECHNIC UNIVERSITY   (United States)

^e UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AMERICAN PHYSICAL SOCIETY (APS); ANTIFERROMAGNET; CLUSTER ALGORITHMS; DISORDERED PHASE; FERROMAGNET (FM); HIGH TEMPERATURE (HT); KAGOME LATTICES; LATTICE (CO); LONG RANGE ORDER (LRO); LOW TEMPERATURE (LTR); MONTE CARLO SIMULATION (MCS); PHYSICAL REGION; STATE MODELING; TRANSITION (JEL CLASSIFICATIONS:E52 ,E41 ,E31); UNIVERSALITY CLASS; ZERO TEMPERATURES;

ANTIFERROMAGNETIC MATERIALS;

EID: 47949100636     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.101.030601     Document Type: Article

References (32)

1. R.B. Potts, Proc. Cambridge Philos. Soc. 48, 106 (1952). PCPSA4 0008-1981
2. F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982); RMPHAT 0034-6861 10.1103/RevModPhys.54.235
3. F.Y. Wu Rev. Mod. Phys. 55, 315(E) (1983); RMPHAT 0034-6861 10.1103/RevModPhys.55.315
4. F.Y. Wu, J. Appl. Phys. 55, 2421 (1984). JAPIAU 0021-8979 10.1063/1.333682
5. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).
6. B. Nienhuis, J. Stat. Phys. 34, 731 (1984). JSTPSB 0022-4715 10.1007/BF01009437
7. P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (Springer-Verlag, New York, 1997).
8. Some exceptions are the Ising model (q=2) on the triangular lattice (qc=4), which has a zero-temperature critical point [J. Stephenson, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 5, 1009 (1964)], and the Ising model on the kagome lattice (qc=3), which is noncritical at all temperatures, including zero temperature. 10.1063/1.1704202
9. I. Syozi, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M.S. Green, (Academic, London, 1972), Vol. 1.
10. See J. Salas and A.D. Sokal, J. Stat. Phys. 92, 729 (1998), and the references cited there. JSTPSB 0022-4715 10.1023/A:1023002322985
11. Some exceptions are the constrained square-lattice 4-state antiferromagnetic Potts model and the triangular-lattice antiferromagnetic spin-s Ising model for large enough s [C. Zeng and C.L. Henley, Phys. Rev. B PRBMDO 0163-1829 55, 14935 (1997)], both of which appear to lie in a noncritical ordered phase at zero temperature. 10.1103/PhysRevB.55.14935
12. J.K. Burton, Jr. and C.L. Henley, J. Phys. A JPHAC5 0305-4470 30, 8385 (1997). 10.1088/0305-4470/30/24/007
13. M. den Nijs, M.P. Nightingale, and M. Schick, Phys. Rev. B RBMDO 0163-1829 26, 2490 (1982). 10.1103/PhysRevB.26.2490
14. J. Kolafa, J. Phys. A JPHAC5 0305-4470 17, L777 (1984). 10.1088/0305-4470/17/14/010
15. D.A. Huse and A.D. Rutenberg, Phys. Rev. B PRBMDO 0163-1829 45, 7536 (1992). 10.1103/PhysRevB.45.7536
16. J. Kondev and C.L. Henley, Nucl. Phys. NUPBBO 0550-3213 B464, 540 (1996). 10.1016/0550-3213(96)00064-8
17. C. Moore and M.E.J. Newman, J. Stat. Phys. 99, 629 (2000). JSTPSB 0022-4715 10.1023/A:1018638624854
18. J. Kondev and C.L. Henley, Phys. Rev. B PRBMDO 0163-1829 52, 6628 (1995). 10.1103/PhysRevB.52.6628
19. I. Jensen, A.J. Guttmann, and I.G. Enting, J. Phys. A JPHAC5 0305-4470 30, 8067 (1997). 10.1088/0305-4470/30/23/008
20. H. Feldmann, R. Shrock, and S.-H. Tsai, Phys. Rev. E 57, 1335 (1998). PLEEE8 1063-651X 10.1103/PhysRevE.57.1335
21. The idea of integrating out one sublattice goes back at least to R. Kotecký, Phys. Rev. B PRBMDO 0163-1829 31, 3088 (1985). 10.1103/PhysRevB.31.3088
22. I. Jensen, J. Phys.: Conf. Ser. 42, 163 (2006); 1742-6588 10.1088/1742-6596/42/1/016
23. http://www.ms.unimelb.edu.au/~iwan/polygons/Polygons_ser.html.
24. This bound combines the isoperimetric inequality qn(1)≤(n2/36)qn (where qn is the number of n-step hexagonal-lattice SAPs modulo translation), the elementary bound qn≤μn-2 (which follows from the supermultiplicativity qm+n-2qmqn, provable by concatenation), and the bound μ<1.868832 [S.E. Alm and R. Parviainen, J. Phys. A JPHAC5 0305-4470 37, 549 (2004)]. 10.1088/0305-4470/37/3/001
25. R. Kotecký, J. Salas, and A.D. Sokal (to be published).
26. J.-S. Wang, R.H. Swendsen, and R. Kotecký, Phys. Rev. Lett. 63, 109 (1989); PRLTAO 0031-9007 10.1103/PhysRevLett.63.109
27. J.-S. Wang R.H. Swendsen R. Kotecký Phys. Rev. B PRBMDO 0163-1829 42, 2465 (1990). 10.1103/PhysRevB.42.2465
28. S.J. Ferreira and A.D. Sokal, J. Stat. Phys. 96, 461 (1999). JSTPSB 0022-4715 10.1023/A:1004599121565
29. J. Salas and A.D. Sokal, J. Stat. Phys. 87, 1 (1997); JSTPSB 0022-4715 10.1007/BF02181478
30. T.M. Garoni, G. Ossola, M. Polin, and A.D. Sokal (to be published).
31. A.D. Sokal, in Surveys in Combinatorics, 2005, edited by, B.S. Webb, (Cambridge University Press, Cambridge, England, 2005).
32. J.C. Wierman, J. Phys. A JPHAC5 0305-4470 35, 959 (2002). 10.1088/0305-4470/35/4/308