Related papers: Dimensional reduction and its breakdown in the dri…
We study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional…
We investigate the critical behavior of disordered systems transversely driven at a uniform and steady velocity. An intuitive argument predicts that the long-distance physics of $D$-dimensional driven disordered systems at zero temperature…
We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…
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…
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.…
Recent work on exact renormalization group flow equations has pointed out the possibility to study critical phenomena in continuous dimension D of space. In an investigation of the O(N) model the dimension N of the fields may be seen as a…
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…
We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of…
In a wide class of D-dimensional spacetimes which are direct or semi-direct sums of a (D-n)-dimensional space and an n-dimensional homogeneous ``internal'' space, a field can be decomposed into modes. As a result of this mode decomposition,…
The concept of dimensional reduction in the high temperature regime is generalized to static Green's functions of composite operators that contain fermionic fields. The recognition of a natural kinematic region where the lowest Matsubara…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical…
We generalize the concept of dimensional reduction to operators involving fermion fields in high temperature field theories. It is found that the ultraviolet behavior of the running coupling constant plays a crucial role. The general…
We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
$O(N)$ invariant vector models have been shown to possess non-trivial scaling large $N$ limits, at least perturbatively within the loop expansion, a property they share with matrix models of 2D quantum gravity. In contrast with matrix…
We investigate the critical behavior and the nature of the low-temperature phase of the $O(N)$ models treating the number of field components $N$ and the dimension $d$ as continuous variables with a focus on the $d\leq 2$ and $N\leq 2$…
We consider the effective potential in three-dimensional models with O(N) symmetry. For generic values of N, and in particular for the physically interesting cases N=0,1,2,3, we determine the six-point and eight-point renormalized coupling…
We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the…
We provide a theoretical analysis by means of the nonperturbative functional renormalization group (NP-FRG) of the corrections to scaling in the critical behavior of the random-field Ising model (RFIM) near the dimension $d_{DR}\approx 5.1$…