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

Gilles Tarjus (1) , Matthieu Tissier (1)

1 LPTL - Laboratoire de Physique Théorique des Liquides

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.

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Gilles Tarjus, Matthieu Tissier. Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction. Physical Review Letters, 2004, 93, pp.267008. ⟨10.1103/PhysRevLett.93.267008⟩. ⟨hal-00003001v2⟩