Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-05-19
J.Statist.Phys. 108 (2002) 213-246
Physics
Condensed Matter
Statistical Mechanics
38 pages, 14 figures, uses revtex, modified presentation for a generic spin model, calculation of subleading amplitude added
Scientific paper
We propose to combine the nonlinear scaling fields associated with the high-temperature (HT) fixed point, with those associated with the unstable fixed point, in order to calculate the susceptibility and other thermodynamic quantities. The general strategy relies on simple linear relations between the HT scaling fields and the thermodynamic quantities, and the estimation of RG invariants formed out of the two sets of scaling fields. This estimation requires convergent expansions in overlapping domains. If, in addition, the initial values of the scaling fields associated with the unstable fixed point can be calculated from the temperature and the parameters appearing in the microscopic Hamiltonian, one can estimate the critical amplitudes. This strategy has been developed using Dyson's hierarchical model where all the steps can be approximately implemented with good accuracy. We show numerically that for this model (and a simplified version of it), the required overlap apparently occurs, allowing an accurate determination of the critical amplitudes.
Meurice Yannick
Niermann S.
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