Discontinuity of the percolation density in one dimensional 1/|x-y|2 percolation models

Communications in Mathematical Physics

Volumn 107, Issue 4, 1986, Pages 611-647

  Aizenman, M ^a   Newman, C M ^b  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000847052     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/BF01205489     Document Type: Article

References (26)

1. Long-range order in one-dimensional Ising systems
2. Exact results in the Kondo problem. II. Scaling theory, qualitatively correct solution, and some new results on one-dimensional classical statistical models
3. Some numerical results on the Kondo problem and the inverse square one-dimensional Ising model
4. One dimensional 1/| j−i|s percolation models: The existence of a transition for s≦2
5. The phase transition in the one-dimensional Ising model with 1/r2 interaction energy
6. Tree graph inequalities and critical behavior in percolation models
7. Rigorous entropy-energy arguments
8. Some properties of a one-dimensional Ising chain with an inverse-square interaction
9. Correlation inequalities and the decay of correlations in ferromagnets
10. Renewal sets and random cutouts
11. Correlation inequalities on some partially ordered sets
12. Approximating many server queues by means of single server queues
13. Association of random variables with applications
14. Percolation processes. Lower bounds for the critical probability
15. Decay of correlations in classical lattice models at high temperature
16. A refinement of Simon's correlation inequality
17. Infinite clusters in percolation models
18. On the continuity of the magnetization and energy in Ising ferromagnets