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Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction

Gilles Tarjus·Matthieu Tissier
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Abstract

We have developed a non-perturbative functional renormalization group approach for the random field O(N) model (RFO(N)M) that allows us to investigate the ordering transition in any dimension and for any value of N including the Ising case. We show that the failure of dimensional reduction and standard perturbation theory is due to the non-analytic nature of the zero-temperature fixed point controlling the critical behavior, non-analycity which is associated with the existence of many metastable states. We find that this non-analycity leads to critical exponents differing from the dimensional reduction prediction only below a critical dimension d\_c(N)<6, with d\_c(N=1)>3.

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Gilles Tarjus, Matthieu Tissier. 2005-01-20. Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction. https://doi.org/10.1103/physrevlett.93.267008

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