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Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems | Gilles Tarjus
; Maxime Baczyk
; Matthieu Tissier
; | Date: |
14 Sep 2012 | Abstract: | We investigate the connection between a formal property of the critical
behavior of several systems in the presence of quenched disorder, known as
"dimensional reduction", and the presence in the same systems at zero
temperature of collective events known as "avalanches". Avalanches generically
produce nonanalyticities in the functional dependence of the cumulants of the
renormalized disorder. We show that this leads to a breakdown of the
dimensional reduction predictions if and only if the fractal dimension
characterizing the scaling properties of the avalanches is exactly equal to the
difference between the dimension of space and the scaling dimension of the
primary field, e.g. the magnetization in a random field model. This is proven
by combining scaling theory and functional renormalization group. We therefore
clarify the puzzle of why dimensional reduction remains valid in random field
systems above a nontrivial dimension (but fails below), always applies to the
statistics of branched polymer and is always wrong in elastic models of
interfaces in a random environment. | Source: | arXiv, 1209.3161 | Services: | Forum | Review | PDF | Favorites |
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