Related papers: Critical Exponents from Field Theory: New Evaluati…
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 investigate the critical dynamics of O(N)-symmetric scalar field theories to determine the critical exponents of transport coefficients as a second-order phase transition is approached from the symmetric phase. A set of stochastic…
The field-theoretical renormalization group approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g_6 and g_8 for the O(n)-symmetric model. The RG series for g_6 and g_8 are…
We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants,…
The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent…
Self-similar approximation theory allows for defining effective sums of asymptotic series. The method of self-similar factor approximants is applied for calculating the critical temperature and critical exponents of the $O(N)$-symmetric…
In this work, we use a specific parameterization of the hypergeometric approximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) to approximate the seven-loop critical exponent $\nu$ for the $O(2)$-symmetric $\phi^4$…
We shortly illustrate how the field-theoretic approach to critical phenomena takes place in the more complete Wilson theory of renormalization and qualitatively discuss its domain of validity. By the way, we suggest that the differential…
We compute the critical exponents of the O(N) model within the Functional Renormalization Group (FRG) approach. We use recent advances which are based on the observation that the FRG flow equation can be put into the form of an…
There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4<d<6 and for large N. Using the functional renormalization group equation, we show that in the lowest order of the…
Generalizing methods developed by Pinn, Pordt and Wieczerkowski for the hierarchical model with one component (N=1) and dimensions d between 2 and 4 we compute O(N)-symmetric fixed points of the hierarchical renormalization group equation…
We consider $O(N)$-symmetric bosonic $\phi^4$ field theories above four dimensions, and propose a new reformulation in terms of an irreducible tensorial field with a cubic and Yukawa terms. The $\phi^4$ field theory so rewritten exhibits…
In renormalized field theories there are in general one or few fixed points which are accessible by the renormalization-group flow. They can be identified from the fixed-point equations. Exceptionally, an infinite family of fixed points…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated on the base of six-loop renormalization-group (RG) expansions. A simple Pade-Borel technique is used for the resummation of the RG series and the Pade approximants…
Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New…
A self-consistent renormalization group flow equation for the scalar lambda phi^4 theory is analyzed and compared with the local potential approximation. The two prescriptions coincide in the sharp cutoff limit but differ with a smooth…
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In…
Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a $\phi^4$-type scalar field theory involving two real scalar fields (one is heavy with mass $M$ and the other light). Then, to all orders…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…