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 <or=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 <or=1/2, confirming the belief that all exponents take on their classical values in the Gaussian, renormalization group fixed point, regime.