The critical behaviour of disordered magnetic systems-an exactly solvable model
- 14 June 1976
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 9 (11) , 2103-2120
- https://doi.org/10.1088/0022-3719/9/11/018
Abstract
Exact analytic results are presented for the critical properties of the dilute Ising model on a Bethe lattice, where a fraction p of the sites are occupied at random by spins. It is found that the critical behaviour is the same as that of the pure system (p=1) except for transitions which occur by varying p at zero temperature, where the critical behaviour is different and corresponds to the percolation problem. For T to 0 and p to pc, the percolation concentration, the zero-field magnetization shows crossover behaviour of the form expected from scaling theories. Outside the critical region, a rapidly convergent numerical method is developed and used to calculate the spontaneous magnetization.Keywords
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