Journal article
From Nonlinear Scaling Fields to Critical Amplitudes
Journal of statistical physics, Vol.108(1), pp.213-246
07/2002
DOI: 10.1023/A:1015495620036
Abstract
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.
Details
- Title: Subtitle
- From Nonlinear Scaling Fields to Critical Amplitudes
- Creators
- Y Meurice - University of IowaS Niermann - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of statistical physics, Vol.108(1), pp.213-246
- Publisher
- Kluwer Academic Publishers-Plenum Publishers
- DOI
- 10.1023/A:1015495620036
- ISSN
- 0022-4715
- eISSN
- 1572-9613
- Language
- English
- Date published
- 07/2002
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984199772502771
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