Dobrushin interfaces via reflection positivity

Communications in Mathematical Physics

Volumn 276, Issue 3, 2007, Pages 827-861

  Shlosman, Senya ^a,b   Vignaud, Yvon ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35548975175     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0308-1     Document Type: Article

References (20)

1. Aizenman M. (1994). On the slow decay of O(2) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model. J. Stat. Phys. 77: 351-359
2. Cerny J. and Kotecky R. (2003). Interfaces for random cluster models. J. Stat. Phys. 111: 73-106
3. Dobrushin R.L. (1972). Gibbs state, describing the coexistence of phases in the three-dimensional Ising model. Th. Prob. and its Appl. 17: 582-600
4. Dobrushin R.L. and Shlosman S. (1981). Phases corresponding to the local minima of the energy. Selecta Math. Soviet. 1(4): 317-338
5. Dold A. (1995). Lectures on Algebraic Topology. Springer, Berlin-Heidelberg-New York
6. Fröhlich J., Israel R., Lieb E. and Simon B. (1978). Phase transitions and reflection positivity I. Commun. Math. Phys. 62: 1-34
7. Fröhlich J. and Lieb E.H. (1978). Phase transitions in anisotropic lattice spin systems. Commun. Math. Phys. 60(3): 233-267
8. Fröhlich J. and Pfister C.-E. (1983). Spin waves, vortices and the structure of equilibrium states in the classical XY model. Commun. Math. Phys. 89: 303-327
9. Frohlich J., Simon B. and Spencer T. (1976). Infrared bounds, phase transitions and continuous symmetry breaking. Commun. Math. Phys. 50: 79
10. Frohlich J. and Spencer T. (1981). The Kosterlitz- Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas. Commun. Math. Phys. 81: 527-602
11. Grimmett, G.: Private communication
12. Gielis G. and Grimmett G. (2002). Rigidity of the Interface in Percolation and Random-Cluster Models. J. Stat. Phys. 109(1-2): 1-37
13. Holicky P., Kotecky R. and ZahradnIk M. (1988). Rigid interfaces for lattice models at low temperatures. J. Stat. Phys. 50: 755-812
14. Kenyon R. (2001). Dominos and the Gaussian free field. Ann. Prob. 29(3): 1128-1137
15. Shlosman S. and van Enter A.C.D. (2002). First-Order Transitions for n-Vector Models in Two and More Dimensions: Rigorous Proof. Phys. Rev. Lett. 89: 285702
16. Shlosman S. and van Enter A.C.D. (2005). Provable First-Order Transitions for Nonlinear Vector and Gauge Models with Continuous Symmetries. Commun. Math. Phys. 255(1): 21-32
17. Shlosman S. (1986). The Method of Reflection Positivity in the Mathematical Theory of First-Order Phase Transitions. Russ. Math. Surv. 41(3): 83-134
18. Shlosman, S., Vignaud, Y.: Rigidity of the interface between low-energy and high-entropy phases. In preparation
19. Vignaud, Y.: Entropic repulsion and entropic attraction. In preparation
20. Vignaud, Y.: Rigidity of the interface for a continuous symmetry model in a slab. In preparation