Potentials for one-dimensional restrictions of Gibbs measures. (English) Zbl 1016.82008
Miracle-Solé, Salvador (ed.) et al., Mathematical results in statistical mechanics. Proceedings, Marseille, France, July 27-31, 1998. Singapore: World Scientific. 485-500 (1999).
Summary: We discuss restrictions of two-dimensional translation-invariant Gibbs measures to a one-dimensional layer. We prove that there exists a translation invariant a.s. absolutely convergent potential making these restrictions into weakly Gibbsian measures. We discuss the existence of the thermodynamic functions for this potential and the variational principle for the weakly Gibbsian measures. See also C. Maes, F. Redig and A. Van Moffaert [Stoch. Process. Appl. 79, 1-15 (1999; Zbl 0963.60094); J. Stat. Phys. 96, 69-107 (1999; Zbl 0964.82008)].
For the entire collection see [Zbl 0926.00032].
For the entire collection see [Zbl 0926.00032].
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60G60 | Random fields |
