Related papers: Analyticity of critical exponents of the $O(N)$ mo…

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 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…

Within the framework of field-theoretical description of second-order phase transitions via the 3-dimensional O(N) vector model, accurate predictions for critical exponents can be obtained from (resummation of) the perturbative series of…

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 reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…

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 consider dimensional crossover for an O(N) model on a d-dimensional layered geometry of thickness L, in the sigma-model limit, using ``environmentally friendly'' renormalization. We show how to derive critical temperature shifts, giving…

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…

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.…

In the framework of the 1/N-expansion we show that the Callan-Symanzik beta- function associated with the four-point coupling g is non-analytic at its zero, i.e. at the fixed-point value g^* of g. This behavior can be interpreted by…

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 show that at $N=\infty$ and below its upper critical dimension, $d<d_{\rm up}$, the critical and tetracritical behaviors of the O($N$) models are associated with the same renormalization group fixed point (FP) potential. Only their…

We complete the analysis of the extremal eigenvalues of the the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph $G(N,d/N)$ in the critical regime $d \asymp \log N$ of the transition uncovered in [arXiv:1704.02953,arXiv:1704.02945],…

We compute the large $N$ critical exponents $\eta$, $\eta_\phi$ and $1/\nu$ in $d$-dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of $1/N$. For instance, the large $N$ conformal bootstrap method is used to…

The critical behavior of the random-field Ising model has been a puzzle for a long time. Different theoretical methods predict that the critical exponents of the random-field ferromagnet in D dimensions are the same as in the pure…

Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…

The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model…

The determination of the critical exponents by means of the Exact Renormalizion Group approach is still a topic of debate. The general flow equation is by construction scheme independent, but the use of the truncated derivative expansion…

We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…

We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents…