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We use polynomial truncations of the Fourier transform of the local measureto calculate the connected q-point functions of Dyson's hierarchical model inthe broken symmetry phase. We show that accurate values of the connected 1, 2and 3 point functions can be obtained at large volume and in a limited range ofconstant external field coupled linearly to the field variable. We introduce anew method to obtain the correct infinite volume and zero external fieldextrapolations. We extract the leading critical exponents and show that theyobey the scaling and hyperscaling relations with an accuracy ranging from 10^-5to 5 10^-3. We briefly discuss how to improve the method of calculation.Comment: 32 pages, 14 figures, Revte

Hyperscaling in the broken symmetry phase of Dyson’s hierarchical model