Critical behaviour of the random-field Ising model with long-range interactions in one dimension

We study the critical behaviour of the 1D random field Ising model (RFIM) with long-range interactions (∝ r−(d+σ)) by the nonperturbative functional renormalization group. We find two distinct regimes of critical behaviour as a function of σ, separated by a critical value σc. What distinguishes thes...

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Bibliographic Details
Published in:Journal of statistical mechanics 2014-10, Vol.2014 (10), p.P10017-21
Main Authors: Balog, Ivan, Tarjus, Gilles, Tissier, Matthieu
Format: Article
Language:English
Subjects:
Avalanches
Fields (mathematics)
Ising model
Lattices
Mathematical models
Simulation
Statistical mechanics
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Summary:We study the critical behaviour of the 1D random field Ising model (RFIM) with long-range interactions (∝ r−(d+σ)) by the nonperturbative functional renormalization group. We find two distinct regimes of critical behaviour as a function of σ, separated by a critical value σc. What distinguishes these two regimes is the presence or not of a cusp-like nonanalyticity in the functional dependence of the renormalized cumulants of the random field at the fixed point. This change of behaviour can be associated with the characteristics of the large-scale avalanches present in the system at zero temperature. We propose some ways to check these predictions through lattice simulations. We also discuss the differences with the RFIM on the Dyson hierarchical lattice.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2014/10/P10017