Electronic Journal of Probability
- Electron. J. Probab.
- Volume 6 (2001), paper no. 6, 27 pp.
Strict Inequality for Phase Transition between Ferromagnetic and Frustrated Systems
We consider deterministic and disordered frustrated systems in which we can show some strict inequalities with respect to related ferromagnetic systems. A case particularly interesting is the Edwards-Anderson spin-glass model in which it is possible to determine a region of uniqueness of the Gibbs measure, which is strictly larger than the region of uniqueness for the related ferromagnetic system. We analyze also deterministic systems with $|J_b| \in [J_A, J_B]$ where $0 \lt J_A \leq J_B \lt \infty$, for which we prove strict inequality for the critical points of the related FK model. The results are obtained for the Ising models but some extensions to Potts models are possible.
Electron. J. Probab., Volume 6 (2001), paper no. 6, 27 pp.
Accepted: 7 February 2001
First available in Project Euclid: 19 April 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82B26: Phase transitions (general)
Secondary: 82B31: Stochastic methods 82B43: Percolation [See also 60K35] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
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De Santis, Emilio. Strict Inequality for Phase Transition between Ferromagnetic and Frustrated Systems. Electron. J. Probab. 6 (2001), paper no. 6, 27 pp. doi:10.1214/EJP.v6-79. https://projecteuclid.org/euclid.ejp/1461097636