Electronic Journal of Probability

Strict Inequality for Phase Transition between Ferromagnetic and Frustrated Systems

Emilio De Santis

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 6 (2001), paper no. 6, 27 pp.

Dates
Accepted: 7 February 2001
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097636

Digital Object Identifier
doi:10.1214/EJP.v6-79

Mathematical Reviews number (MathSciNet)
MR1825713

Zentralblatt MATH identifier
1050.82020

Subjects
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

Keywords
Phase transition Ising model disordered systems stochastic order

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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