Avalanches and perturbation theory in the random-field Ising model. (25th February 2016)

• Record Type: Journal Article
• Authors: Tarjus, Gilles; Tissier, Matthieu
• Is Part Of: Journal of statistical mechanics. (2016:Feb.)
• Publication Date: 2016-02-25
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/02/023207
• Languages: English
• ISSNs: 1742-5468

Abstract

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 dimensions. 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 dimensions 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.