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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Statistical Mechanics: Theory and Experiment
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
