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Avalanches and perturbation theory in the random-field Ising model | | Gilles Tarjus
; Matthieu Tissier
; | | Date: |
6 Oct 2015 | | Abstract: | Perturbation theory for the random-field Ising model (RFIM) has the infamous
attribute that it predicts at all orders a dimensional-reduction property for
the critical behavior that turns out to be wrong in low dimension. Guided by
our previous work based on the nonperturbative functional renormalization group
(NP-FRG), we show that one can still make some use of the perturbation theory
for a finite range of dimension below the upper critical dimension, d=6. The
new twist is to account for the influence of large-scale zero-temperature
events known as avalanches. These avalanches induce nonanalyticities in the
field dependence of the correlation functions and renormalized vertices, and we
compute in a loop expansion the eigenvalue associated with the corresponding
anomalous operator. The outcome confirms the NP-FRG prediction that the
dimensional-reduction fixed point correctly describes the dominant critical
scaling of the RFIM above some dimension close to 5 but not below. | | Source: | arXiv, 1510.1718 | | Services: | Forum | Review | PDF | Favorites | |
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