Non-Universal Quantities from Dual RG Transformations

Details Non-Universal Quantities from Dual RG Transformations Non-Universal Quantities from Dual RG Transformations

1999-04-03

arxiv.org/abs/hep-lat/9904002v1

Phys.Rev. E60 (1999) 2612-2615

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, 1 figure, uses revtex

Scientific paper

10.1103/PhysRevE.60.2612

Using a simplified version of the RG transformation of Dyson's hierarchical model, we show that one can calculate all the non-universal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under the RG transformation and has a smooth limit in the high-temperature limit. Using the analogy with hamiltonian systems, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be tought of as coupled oscillators allowing resonance phenomena.

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