Critical isotherm of Dyson's hierarchical model
- 1 June 1977
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 10 (6) , L125-L128
- https://doi.org/10.1088/0305-4470/10/6/007
Abstract
The critical isotherm for Dyson's (1969) hierarchical model in one dimension with potential decaying as r(-1+ sigma ) is investigated in the classical regime 0< sigma 1/2, corresponding to a Gaussian fixed point of the exact renormalization group equation. Exact series expansions for the magnetization at the critical point are developed and analysed. It is concluded that delta =3.0+or-0.05 for 0< sigma 1/2, confirming the belief that all exponents take on their classical values in the Gaussian, renormalization group fixed point, regime.Keywords
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