Power-law corrections to exponential decay of connectivites and correlations in lattice models

Annals of Probability

Volumn 29, Issue 1, 2001, Pages 92-122

  Alexander, Kenneth S ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Exponential decay; FK model; Ornstein Zernike behavior; Power law correction; Weak mixing

Indexed keywords

EID: 0035533095     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1008956323     Document Type: Article

References (21)

1. 2 Ising and Potts models. J. Statist. Phys. 50 1-10.
2. ALEXANDER, K. S. (1990). Lower bounds on the connectivity function in all directions for Bernoulli percolation in two and three dimensions. Ann. Probab. 18 1547-1562.
3. ALEXANDER, K. S. (1992). Stability of the Wulff minimum and fluctuations in shape for large finite clusters in two-dimensional percolation. Probab. Theory Related Fields 91 507-532.
4. ALEXANDER, K. S. (1997). Approximation of subadditive functions and convergence rates in limiting shape results. Ann. Probab. 25 30-55.
5. ALEXANDER, K. S. (1997). The asymmetric random cluster model and comparison of Ising and Potts models. Probab. Theory Related Fields. To appear.
6. ALEXANDER, K. S (1998). On weak mixing in lattice models. Probab. Theory Related Fields 110 441-471.
7. ALEXANDER, K. S., CHAYES, J. T. and CHAYES, L. (1990). The Wulff construction and asymptotics of the finite cluster distribution for two dimensional Bernoulli percolation. Comm. Math. Phys. 131 1-50.
8. VAN DEN BERG, J. and KESTEN, H. (1985). Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 556-569.
9. BRICMONT, J. and FRÖLICH, J. (1985). Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models. Comm. Math. Phys. 98 553-578.
10. CAMPANINO, M., CHAYES, J. T. and CHAYES, L. (1991). Gaussian fluctuations of connectivities in the subcritical regime of percolation. Probab. Theory Related Fields 88 269-341.
11. d. Unpublished manuscript.
12. CHAYES, J. T. and CHAYES, L. (1986). Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures. Comm. Math. Phys. 105 221-238.
13. FORTUIN, C. M. and KASTELEYN, P. W. (1972). On the random cluster model. I. Introduction and relation to other models. Physica 57 536-564.
14. GRIMMETT, G. R. (1995). The stochastic random-cluster process and uniqueness of random-cluster measures. Ann. Probab. 23 1461-1510.
15. GRIMMETT, G. R. (1997). Percolation and disordered systems. Lectures on Probability Theory and Statistics. Lecture Notes in Math. 1665 153-300. Springer, New York.
16. HARRIS, T. (1960). A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 13-20.
17. d. Unpublished manuscript. Markov Processes and Related Fields 4 323-350.
18. LAANAIT, L., MESSAGER, A. and RUIZ, J. (1986). Phase coexistence and surface tensions for the Potts model. Comm. Math. Phys. 105 527-545.
19. MCCOY, B. M. and WU, T. T. (1973). The Two-Dimensional Ising Model. Harvard Univ. Press.
20. ORNSTEIN, L. S. and ZERNIKE, F. (1914). Accidental deviations of density and opalescence at the critical point of a single substance. Proc. Acad. Sci. (Amst.) 17 793-806.
21. PFISTER, C.-E. and VELENIK, Y. (1997). Large deviations and continuum limit in the 2D Ising model. Probab. Theory Related Fields 109 435-506.