Rigorous bounds for 2D disordered ising models
- 1 January 1986
- journal article
- Published by EDP Sciences in Journal de Physique
- Vol. 47 (6) , 947-953
- https://doi.org/10.1051/jphys:01986004706094700
Abstract
A method systematically improving the annealed bounds (for the free energy and the ground state energy) is presented and illustrated by the example of disordered Ising models. An optimization procedure leads to new bounds for which the critical behaviour differs from the pure model behaviour. Geometrical effects, such as frustration, can also be included in this method. We obtain simple expressions for the critical lines which agree remarkably well with previously known exact resultsKeywords
This publication has 11 references indexed in Scilit:
- Critical frontiers associated with the bond-diluted Ising ferromagnet on triangular and honeycomb latticesJournal of Physics C: Solid State Physics, 1982
- Random antiphase state and frustration in two dimensionsJournal de Physique Lettres, 1982
- Cluster extension of the effective-interaction approximation. I. Quenched-bond disorder in the Ising modelJournal of Physics C: Solid State Physics, 1980
- Exact results and critical properties of the Ising model with competing interactionsJournal of Physics C: Solid State Physics, 1980
- Renormalisation group attemts to obtain the transition line of the square-lattice bond-dilute Ising modelJournal of Physics C: Solid State Physics, 1980
- Effect of random defects on the critical behaviour of Ising modelsJournal of Physics C: Solid State Physics, 1974
- Plural Transitions for an Ising Model of a Mixture of Ferromagnetic and Antiferromagnetic BondsProgress of Theoretical Physics, 1973
- Renormalization of Critical Exponents by Hidden VariablesPhysical Review B, 1968
- Some Exact Critical Percolation Probabilities for Bond and Site Problems in Two DimensionsPhysical Review Letters, 1963
- Order-disorder in hexagonal latticesPhysica, 1950