Critical properties of loop percolation models with optimization constraints

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 5 2, 2003, Pages

  Pfeiffer, Frank O ^a   Rieger, Heiko ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CALCULATIONS; FUNCTIONS; GROUND STATE; HAMILTONIANS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; OPTIMIZATION; PHASE TRANSITIONS; PROBABILITY DISTRIBUTIONS; THREE DIMENSIONAL; TWO DIMENSIONAL;

DISORDER STRENGTH; ENERGY FUNCTION; LATTICE DIVERGENCE OPERATOR; LOOP HAMILTONIAN MODEL; OPTIMIZATION CONSTRAINTS; PERCOLATION TRANSITION; PERIODIC BOUNDARY CONDITION;

PERCOLATION (FLUIDS);

EID: 42749098554     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. G.A. Williams, Phys. Rev. Lett. 59, 1926 (1987), and references cited therein.
2. A.M.J. Schakel, Phys. Rev. E 63, 026115 (2001).
3. G.A. Williams, Phys. Rev. Lett. 82, 1201 (1999), and references cited therein.
4. Karl Strobl and Mark Hindmarsh, Phys. Rev. E 55, 1120 (1997).
5. A. K. Nguyen and A. Sudbø, Phys. Rev. B 58, 2802 (1998).
6. F.O. Pfeiffer and H. Rieger, J. Phys.: Condens. Matter 14, 2361 (2002).
7. S.T. Chui and J.D. Weeks, Phys. Rev. B 14, 4987 (1976).
8. J. Toner, Phys. Rev. Lett. 66, 679 (1991).
9. H. Rieger and U. Blasum, Phys. Rev. B 55, 7394 (1997).
10. D. Stauffer, Introduction to Percolation Theory (Taylor & Francis, London, 1985)
11. A. Bunde and S. Havlin, Fractals and Disordered Systems, 2nd ed. (Springer, New York, 1996).
12. J. Kisker and H. Rieger, Phys. Rev. B 58, R8873 (1998)
13. F. Pfeiffer and H. Rieger, ibid. 60, 6304 (1999).
14. F.O. Pfeiffer and H. Rieger, J. Phys. A 13, 2489 (2000).
15. C. Zeng, J. Kondev, D. McNamara, and A.A. Middleton, Phys. Rev. Lett. 80, 109 (1998).
16. A. Hartmann and H. Rieger, Optimization Algorithms in Physics (Wiley-VCH, Berlin, 2002).
17. H.S. Bokil and A.P. Young, Phys. Rev. Lett. 74. 3021 (1995).
18. J.M. Kosterlitz and M.V. Simkin, Phys. Rev. Lett. 79, 1098 (1997).
19. N. Kawashima and N. Ito, J. Phys. Soc. Jpn. 62, 435 (1993).
20. M.E. Fisher, Physics 3, 255 (1967).
21. Y. Leroyer and E. Pommiers, Phys. Rev. B 50, 2795 (1994).
22. J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, 1997).
23. J.M. Kosterlitz and D.J. Touless, J. Phys. C 6, 1181 (1973).
24. We reproduced the results of conventional bond percolation for comparison, where we used parameters (i.e., number of samples and system sizes) similar to the study of the LP model.