ON THE LOWER CRITICAL DIMENSIONALITY OF THE ISING-MODEL IN A RANDOM FIELD
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 combi...
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
1983
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| Shrnutí: | 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. |
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