相关论文: Reply on "Lifshitz-point critical behaviour to $O(…

We reply to a recent comment by Diehl and Shpot (cond-mat/0305131) criticizing a new approach to the Lifshitz critical behavior just presented (M. M. Leite Phys. Rev. B 67, 104415(2003)). We show that this approach is free of…

We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B {\bf 67}, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not…

Generic higher character Lifshitz critical behaviors are described using field theory and $\epsilon_{L}$-expansion renormalization group methods. These critical behaviors describe systems with arbitrary competing interactions. We derive the…

We comment on a recent letter by L. C. de Albuquerque and M. M. Leite (J. Phys. A: Math. Gen. 34 (2001) L327-L332), in which results to second order in $\epsilon=4-d+\frac{m}{2}$ were presented for the critical exponents…

New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8)…

We present the critical exponents $\nu_{L2}$, $\eta_{L2}$ and $\gamma_{L}$ for an $m$-axial Lifshitz point at second order in an $\epsilon_{L}$ expansion. We introduced a constraint involving the loop momenta along the $m$-dimensional…

An introduction to the theory of critical behavior at Lifshitz points is given, and the recent progress made in applying the field-theoretic renormalization group (RG) approach to $\phi^4$ $n$-vector models representing universality classes…

A new renormalization group treatment is proposed for the critical exponents of an m-fold Lifshitz point. The anisotropic cases (m not equal 8) are described by two independent fixed points associated to two independent momentum flow along…

The Lifshitz critical behavior for a single component field theory is studied for the specific isotropic case in the framework of the Functional Renormalization Group. Lifshitz fixed point solutions of the flow equation, derived by using a…

The critical exponents $\nu_{L2}, \eta_{L2}$ and $\gamma_{L2}$ of a uniaxial Lifshitz point are calculated at two-loop level using renormalization group and $\epsilon_{L}$-expansion techniques. We found a new constraint involving the loop…

We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero…

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential…

In this paper, we extend the uniform regularity estimates obtained by M. Avellanda and F. Lin in the paper of Compactness methods in the theory of homogenization (Comm. Pure Appl. Math. 40(1987), no.6, 803-847) to the more general second…

We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with $L$ independent scaling transformations associated to the various…

In this work we investigate the critical behavior of physical systems with competing interactions that present points Lifshitz m-axial. For this study we used the techniques of Quantum Field Theory with Massive Scalar interactions of type…

We analyze the critical behavior of isotropic systems with dipole-dipole interaction by renormalization-group methods in fixed space-time dimensions. Working in three-dimensional theory we analytically find three-loop expressions for…

We employ the derivative expansion of the nonperturbative renormalization group to address the phenomenon of anisotropic scale invariance and the associated functional fixed points, also known as Lifshitz points, in systems characterized by…

This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates…

We describe new universality classes associated to generic higher character Lifshitz critical behaviors for systems with arbitrary short range competing interactions. New renormalization-group arguments are proposed for anisotropic and…

We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…