On the lower critical dimensionality of the Ising model in a random field
- 10 December 1983
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 16 (34) , 6615-6622
- https://doi.org/10.1088/0022-3719/16/34/011
Abstract
The stability of ferromagnetism is studied in the three-dimensional Ising model, in the presence of a static, spatially random magnetic field. An approximation is introduced in which regions with a given spin direction are assumed not to contain smaller clusters of the reverse magnetisation. A combination of the Peierls argument with a rescaling transformation leads to a lower bound for the magnetisation, which is non-zero at low temperatures, provided the random field is not too strong.Keywords
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