Related papers: SCHR\"Odinger Invariance and Strongly Anisotropic …
A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3 ...…
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent theta or a dynamical exponent z. For a given value of theta, we construct local scale transformations which can…
The extension of dynamical scaling to local, space-time dependent rescaling factors is investigated. For a dynamical exponent $z=2$, the corresponding invariance group is the Schr\"odinger group. Schr\"odinger invariance is shown to…
The generalization of dynamical scaling to local scale invariance is reviewed. Starting from a recapitulation of the phenomenology of ageing phenomena, the generalization of dynamical scaling to local scale transformation for any given…
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…
Local scale invariance for lattice models is studied using new realizations of the Schr\"odinger algebra. The two-point function is calculated and it turns out that the result can be reproduced from exact two-point correlation functions…
The scaling functions of single-time and two-time correlators in systems undergoing non-equilibrium critical dynamics with dynamical exponent ${z}=2$ are predicted from a new time-dependent non-equilibrium representation of the…
Local scale-invariance for ageing systems without detailed balance is tested through studying the dynamical symmetries of the critical bosonic contact process and the critical bosonic pair-contact process.Their field-theoretical actions can…
Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…
The dynamical scaling of ageing ferromagnetic systems can be generalized to a local scale invariance. This yields a prediction for the causal two-time response function, which has been numerically confirmed in the Glauber-Ising model…
The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new variant of the Wolff cluster algorithm permits the analysis of systems far larger than in…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
The explicit calculation of the scaling form of the two-time autocorrelation function in phase-ordering kinetics and in those cases of non-equilibrium critical dynamics where the dynamical exponent z=2 through the extension of dynamical…
Physical ageing phenomena far from equilibrium naturally lead to dynamical scaling. It has been proposed to consider the consequences of an extension to a larger Lie algebra of local scale-transformation. The best-tested applications of…
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…
A new variant of the Wolff cluster algorithm is proposed for simulating systems with competing interactions. This method is used in a high-precision study of the Lifshitz point of the 3D ANNNI model. At the Lifshitz point, several critical…
We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we…
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O$(n)$ symmetric anisotropic $\phi^4$ lattice model with periodic boundary conditions in a $d$-dimensional hypercubic geometry above, at and below…