Criticality and crossover in the bond-diluted random Ising model
- 28 April 1978
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 11 (8) , L337-L342
- https://doi.org/10.1088/0022-3719/11/8/008
Abstract
By using the replica trick and a duality transformation, the bond-diluted random Ising model is mapped onto a new Hamiltonian. This demonstrates the higher order critical nature of the percolation point and identifies the appropriate crossover scaling variables. Taking the n to 0 limit of the replica method near the percolation point is shown to be equivalent to the q to 1 limit of the Potts model. The critical line near pc is calculated, yielding for a square lattice exp(-2Kc)=2ln2(p-1/2)+0(p-1/2)2.Keywords
This publication has 15 references indexed in Scilit:
- Rigorous upper and lower bounds on the critical temperature in Ising models with random, quenched, broken-bond disorderJournal of Physics C: Solid State Physics, 1977
- A new approach to the quenched bond-diluted Ising modelJournal of Physics C: Solid State Physics, 1977
- Thermally driven phase transitions near the percolation threshold in two dimensionsJournal of Physics C: Solid State Physics, 1976
- Dilute bond Ising model and percolationJournal of Physics A: General Physics, 1976
- Equivalence of the Potts model or Whitney polynomial with an ice-type modelJournal of Physics A: General Physics, 1976
- Critical properties of many-component systemsPhysical Review B, 1975
- Effect of random defects on the critical behaviour of Ising modelsJournal of Physics C: Solid State Physics, 1974
- Critical Behavior of the Anisotropic-Vector ModelPhysical Review B, 1972
- Scaling Approach to Tricritical Phase TransitionsPhysical Review Letters, 1972
- Some Critical Properties of the Eight-Vertex ModelPhysical Review B, 1971