Mapping all classical spin models to a lattice gauge theory

New Journal of Physics

Volumn 12, Issue , 2010, Pages

  De Las Cuevas, G ^a,b   Dur W ^a,b   Briegel, H J ^a,b   Martin Delgado, M A ^c  

^a UNIVERSITY OF INNSBRUCK   (Austria)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL SPIN MODELS; DISCRETE LATTICES; GAUGE GROUP; HAMILTON FUNCTIONS; LATTICE GAUGE THEORY; PARTITION FUNCTIONS; QUANTUM INFORMATION; STATISTICAL MODELS;

QUANTUM OPTICS; SPIN DYNAMICS;

GAGES;

EID: 77951952293     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/12/4/043014     Document Type: Article

References (38)

1. Wu F Y 1984 Rev. Mod. Phys. 54 235
2. Kogut J B 1979 Rev. Mod. Phys. 51 659
3. Pathria R K 1996 Statistical Mechanics 2nd edn (Oxford: Elsevier)
4. Itzykson C and Drouffe J M. 1991 Statistical Field Theory (Cambridge: Cambridge University Press)
5. Creutz M 1983 Quarks, Gluons and Lattices (Cambridge: Cambridge University Press)
6. Montvay I and Münster G 1994 Quantum Fields on a Lattice (Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press)
7. Van den Nest M, Dür W and Briegel H J 2008 Phys. Rev. Lett. 100 110501
8. De las Cuevas G, Dür W, Van den Nest M and Briegel H J 2009 J. Stat. Mech. P07001
9. De las Cuevas G, Dür W, Briegel H J and Martin-Delgado M A 2009 Phys. Rev. Lett. 102 230502
10. Wegner F 1971 J. Math. Phys. 12 2259
11. Elitzur S 1975 Phys. Rev. D 12 3978
12. Wilson K G 1974 Phys. Rev. D 12 2445
13. Kogut J and Susskind L 1975 Phys. Rev. D 11 395
14. 't Hooft G H 1978 Nucl. Phys. B 138 1
15. Korthals-Altes C, Kovner A and Stephanov M 1999 Phys. Lett. B 469 205
16. Clay Mathematics Institute http://www.claymath.org/millennium/Yang-Mills- Theory
17. Dennis E, Kitaev A, Landahl A and Preskill J 2002 J. Math. Phys. 43 4452
18. Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford: Oxford University Press)
19. Creutz M 1977 Phys. Rev. D 15 1128
20. Van den Nest M, Dür W and Briegel H J 2007 Phys. Rev. Lett. 98 117207
21. Gottesman D 1997 PhD thesis Caltech
22. Van den Nest M 2005 PhD thesis Katholieke Universiteit Leuven
23. Raussendorf R and Briegel H J 2001 Phys. Rev. Lett. 86 5188
24. Wilson K G 1975 Rev. Mod. Phys. 47 773
25. Elitzur S, Pearson R B and Shigemitsu J1979 Phys. Rev. D 19 3698
26. Horn D, Weinstein M and Yankielowicz S 1979 Phys. Rev. D19 3715
27. Ukawa A, Windey P and Guth A H 1980 Phys. Rev. D 21 1013
28. Fröhlich J and Spencer T 1982 Commun. Math. Phys. 83 411
29. Barahona F 1982 J. Phys. A: Math. Gen. 15 3241
30. Aaronson S 2009 The complexity zoo http://qwiki.stanford.edu/wiki/ Complex.ity-Zoo
31. Van den Nest M, Dür W, Raussendorf R and Briegel H J 2009 Phys. Rev. A 80 052334
32. De las Cuevas G et al 2010 Computational complexity of classical lattice models in preparation
33. Drouffe J M 1981 Phys. Lett. B 105 46
34. Flyvberg H, Lautrup B and Zuber J B 1982 Phys. Lett. B 110 279
35. Katzgraber H G, Bombin H and Martin-Delgado M A 2009 Phys. Rev. Lett. 103 090501.
36. Creutz M 2009 private communication
37. Alicki R, Horodecki M, Horodecki P and Horodecki R 2008 arXiv:08.11.0033
38. Bombin H, Chhajlany R W, Horodecki M and Martin-Delgado M A 2009 arXiv:0907.5228