Hyperscaling in the Broken Symmetry Phase of Dyson's Hierarchical Model

Details Hyperscaling in the Broken Symmetry Phase of Dyson's Hierarchical Model Hyperscaling in the Broken Symmetry Phase of Dyson's Hierarchical Model

1999-12-17

arxiv.org/abs/hep-lat/9912032v1

Phys.Rev. D61 (2000) 114509

Physics

High Energy Physics

High Energy Physics - Lattice

32 pages, 14 figures, Revtex

Scientific paper

10.1103/PhysRevD.61.114509

We use polynomial truncations of the Fourier transform of the local measure to calculate the connected q-point functions of Dyson's hierarchical model in the broken symmetry phase. We show that accurate values of the connected 1, 2 and 3 point functions can be obtained at large volume and in a limited range of constant external field coupled linearly to the field variable. We introduce a new method to obtain the correct infinite volume and zero external field extrapolations. We extract the leading critical exponents and show that they obey the scaling and hyperscaling relations with an accuracy ranging from 10^-5 to 5 10^-3. We briefly discuss how to improve the method of calculation.

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