Unexpected spin-off from quantum gravity

Physica A: Statistical Mechanics and its Applications

Volumn 377, Issue 2, 2007, Pages 373-380

  Benedetti, D ^a   Loll, R ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Random geometries; Series expansion; Spin systems

Indexed keywords

CRYSTAL ATOMIC STRUCTURE; GRAPH THEORY; GRAVITATION; THERMAL EXPANSION; THERMODYNAMICS;

RANDOM GEOMETRIES; SERIES EXPANSION; SPIN SYSTEMS; THERMODYNAMIC FUNCTIONS;

QUANTUM THEORY;

EID: 33846700346     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.11.032     Document Type: Article

References (33)

1. C. Domb, Ising model, in: C. Domb, M.S. Green, (Eds.), Phase Transitions and Critical Phenomena, vol. 3, Academic Press, London, 1974, pp. 357-484.
2. Matveev V., and Shrock R. Complex-temperature singularities of the susceptibility in the d = 2 Ising model. I. Square lattice. J. Phys. A 28 (1995) 1557-1583 (hep-lat/9408020)
3. Matveev V., and Shrock R. Complex-temperature singularities in the d = 2 Ising model: triangular and honeycomb lattices. J. Phys. A 29 (1996) 803-823 (hep-lat/9411023 and hep-lat/9412076)
4. Christ N.H., Friedberg R., and Lee T.D. Random lattice field theory. Nucl. Phys. B 202 (1982) 89-125
5. Christ N.H., Friedberg R., and Lee T.D. Gauge theory on a random lattice. Nucl. Phys. B 210 (1982) 310-336
6. Christ N.H., Friedberg R., and Lee T.D. Weights of links and plaquettes in a random lattice. Nucl. Phys. B 210 (1982) 337-346
7. F. David, Simplicial quantum gravity and random lattices, in: Gravitation and Quantizations Les Houches Summer School, Session LVII, 1992, Elsevier, Amsterdam, 1995, pp. 679-750 (hep-th/9303127).
8. Loll R. Discrete approaches to quantum gravity in four dimensions. Liv. Rev. Rel. 1 (1998) 13. http://www.livingreviews.org/lrr-1998-13 〈http://www.livingreviews.org/lrr-1998-13〉
9. Janke W., Johnston D.A., and Villanova R. Spin models on random lattices. Physica A 281 (2000) 207-220
10. Ambjørn J., Jurkiewicz J., and Loll R. The universe from scratch. Contemp. Phys. 47 (2006) 103-117 (hep-th/0509010)
11. Ambjørn J., and Loll R. Non-perturbative Lorentzian quantum gravity, causality and topology change. Nucl. Phys. B 536 (1998) 407-434 (hep-th/9805108)
12. Ambjørn J., Jurkiewicz J., and Loll R. Non-perturbative 3-d Lorentzian quantum gravity. Phys. Rev. D 64 (2001) 044011 (hep-th/0011276)
13. Ambjørn J., Jurkiewicz J., and Loll R. Emergence of a 4D world from causal quantum gravity. Phys. Rev. Lett. 93 (2004) 131301 (hep-th/0404156)
14. Ambjørn J., Anagnostopoulos K.N., and Loll R. A new perspective on matter coupling in 2d quantum gravity. Phys. Rev. D 60 (1999) 104035 (hep-th/9904012)
15. Ambjørn J., Anagnostopoulos K.N., and Loll R. Crossing the c = 1 barrier in 2d Lorentzian quantum gravity. Phys. Rev. D 61 (2000) 044010 (hep-lat/9909129)
16. Ambjørn J., Anagnostopoulos K.N., and Loll R. On the phase diagram of 2d Lorentzian quantum gravity. Nucl. Phys. Proc. Suppl. 83 (2000) 733-735 (hep-lat/9908054)
17. Kazakov V.A. Ising model on a dynamical planar random lattice: exact solution. Phys. Lett. A 119 (1986) 140-144
18. Boulatov D.V., and Kazakov V.A. The Ising model on a random planar lattice: the structure of the phase transition and the exact critical exponents. Phys. Lett. B 186 (1987) 379-384
19. Lima F.W.S., Costa U.M.S., Almeida M.P., and Andrade J.S. Critical behavior of a three-state Potts model on a Voronoi lattice. Eur. Phys. J. B 17 (2000) 111-114 (cond-mat/0008285)
20. Janke W., and Weigel M. The Harris-Luck criterion for random lattices. Phys. Rev. B 69 (2004) 144208 (cond-mat/0310269)
21. D. Benedetti, R. Loll, Quantum gravity and matter: counting graphs on causal dynamical triangulations, preprint University of Utrecht SPIN-06/32, to appear, gr-qc/0611075.
22. Sykes M.F. Some counting theorems in the theory of the Ising model and the excluded volume problem. J. Math. Phys. 2 (1961) 52-62 (Erratum: M.F. Sykes, Some counting theorems in the thoery of the Ising model and the excluded volume problem, J. Math. Phys. 3 (1962) 586)
23. Nagle J.F., and Temperley H.N.V. Combinatorial theorem for graphs on a lattice. J. Math. Phys. 9 (1968) 1020-1026
24. Sykes M.F., Gaunt D.S., Roberts P.D., and Wyles J.A. High-temperature series for susceptibility of Ising-model, 1. 2-dimensional lattices. J. Phys. A 5 (1972) 624-639
25. Hunter D.L., and Baker G.A. Methods of series analysis. I. Comparison of current methods used in the theory of critical phenomena. Phys. Rev. B 7 (1973) 3346-3376
26. A.J. Guttmann, Asymptotic analysis of coefficients in phase transitions and critical phenomena, in: C. Domb, J. Lebowitz, (Eds.), Phase Transitions and Critical Phenomena, vol. 13, Academic Press, London, 1989, pp. 1-234.
27. Janke W., Johnston D.A., and Stathakopoulos M. Fat Fisher zeroes. Nucl. Phys. B 614 (2001) 494-512 (cond-mat/0107013)
28. Guttmann A.J. Ising model susceptibility amplitudes. I. Two-dimensional lattices. J. Phys. A 8 (1975) 1236-1248
29. Thompson C.J., Guttmann A.J., and Ninham B.W. Determination of critical behaviour in lattice statistics from series expansions, II. J. Phys. C 2 (1969) 1889-1899
30. Guttmann A.J. Determination of critical behaviour in lattice statistics from series expansions, III. J. Phys. C 2 (1969) 1900-1907
31. Domb C., and Guttmann A.J. Low temperature series for the Ising model. J. Phys. C 3 (1970) 1652-1660
32. Luck J.M. A classification of critical phenomena on quasi-crystals and other aperiodic structures. Europhys. Lett. 24 (1993) 359-364
33. J. Ambjørn, J. Jurkiewicz, R. Loll, work in progress.