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Article overview
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Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group | | Gilles Tarjus
; Matthieu Tissier
; | | Date: |
8 Oct 2019 | | Abstract: | We review the theoretical description of the random field Ising and $O(N)$
models obtained from the functional renormalization group, either in its
nonperturbative implementation or, in some limits, in perturbative
implementations. The approach solves some of the questions concerning the
critical behavior of random-field systems that have stayed pending for many
years: What is the mechanism for the breakdown of dimensional reduction and the
breaking of the underlying supersymmetry below $d=6$? Can one provide a
theoretical computation of the critical exponents, including the exponent psi
characterizing the activated dynamic scaling? Is it possible to theoretically
describe collective phenomena such as avalanches and droplets? Is the critical
scaling described by 2 or 3 independent exponents? What is the phase behavior
of the random-field $O(N)$ model in the whole ($N$, $d$) plane and what is the
lower critical dimension of quasi-long range order for $N=2$? Are the
equilibrium and out-of-equilibrium critical points of the RFIM in the same
universality class? | | Source: | arXiv, 1910.3530 | | Services: | Forum | Review | PDF | Favorites | |
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