Crossing probabilities in critical 2-D percolation and modular forms

Physica A: Statistical Mechanics and its Applications

Volumn 281, Issue 1, 2000, Pages 242-251

  Kleban, Peter ^a  

^a UNIVERSITY OF MAINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; HEURISTIC METHODS; NUMERICAL METHODS; PERCOLATION (SOLID STATE); PHASE TRANSITIONS; PROBABILITY; TWO DIMENSIONAL;

CONFORMAL FIELD THEORY; CROSSING PROBABILITY; MODULAR FORMS;

STATISTICAL MECHANICS;

EID: 0033686998     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(00)00035-2     Document Type: Article

References (20)

1. Kesten H. Percolation Theory for Mathematicians. 1982;Birkhauser, Boston.
2. Stauffer D., Aharony A. Introduction to Percolation Theory. 1992;Taylor and Francis, London.
3. Kleban P., Ziff R.M. Exact results at the two-dimensional percolation point. Phys. Rev. B. 57:1998;R8075.
4. P. Kleban, D. Zagier, in preparation.
5. Kasteleyn P.W., Fortuin C.M. On the random cluster model I: Introduction and relation to other models. Physica. 57:1972;536-564.
6. Hu C.-K. Physica A. 116:1982;265.
7. Hu C.-K. Physica A. 119:1983;609.
8. Hu C.-K. Phys. Rev. B. 29:1984;5103, 5109.
9. Hu C.-K. Chin. J. Phys. (Taipei). 22:1984;1.
10. Cardy J.L. Critical percolation in finite geometries. J. Phys. A: Math. Gen. 25:1992;L201-206.
11. Cardy J.L. Boundary conditions, fusion rules and the Verlinde formula. Nucl. Phys. B. 324:1989;581.
12. Langlands R., Pichet C., Pouliot P., Saint-Aubin Y. On the universality of crossing probabilities in two-dimensional percolation. J. Stat. Phys. 67:1992;553-574.
13. Langlands R., Pouiliot P., Saint-Aubin Y. Conformal invariance in two-dimensional percolation. Bull. Am. Math. Soc. 30:1994;1-61.
14. R.M. Ziff, Effective boundary extrapolation length, Phys. Rev. E 54 (1996) 2547.
15. Kleban P., Vassileva I. Domain boundary energies in finite regions at 2D criticality via conformal field theory. J. Phys. A. 25:1992;5779-5787.
16. Watts G. A crossing probability for critical percolation in two dimensions. J. Phys. A: Math. Gen. 29:1996;L363.
17. Ziff R.M. On Cardy's formula for the critical crossing probability in 2D percolation. J. Phys. A. 28:1995;1249-1255.
18. Ziff R.M. Proof of crossing formula for 2D percolation. J. Phys. A. 28:1995;6479-6480.
19. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series and Products. 1980;Academic Press, Orlando.
20. Zagier D. Waldschmidt M., Moussa P., Luck J.-M., Itzykson C. From Number Theory to Physics. 1992;Springer, Berlin.