Related papers: Scaling for level statistics from self-consistent …
We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical…
The main purpose of this paper is to study two scaling methods developed respectively by Pinchuk and Frankel. We introduce first a continuously-varying global coordinate system, and give an alternative proof to the convergence of Pinchuk's…
In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Mat\'ern autocovariance in dimension $d>4$. When $d<4$ this is…
This paper relates uniform alpha-Hoelder continuity, or alpha-dimensionality, of spectral measures in an arbitrary interval to the Fourier transform of the measure. This is used to show that scaling exponents of exponential sums obtained…
Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily…
Finite-size scaling expressions for the current near the continuous phase transition, and for the local density near the first-order transition, are found in the steady state of the one-dimensional fully asymmetric simple-exclusion process…
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…
We consider Noncommutative Quantum Mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the…
The possibility of having a delocalization transition in the 1D de Moura-Lyra class of models (having a power-spectrum $\propto q^{-\alpha})$ has been the object of a long standing discussion in the literature, filled with ambiguities. In…
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…
Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a…
The method of scaling algebras, which has been introduced earlier as a means for analyzing the short-distance behaviour of quantum field theories in the setting of the model-independent, operator-algebraic approach, is extended to the case…
The finite-size scaling algorithm based on bulk and surface renormalization of de Oliveira (1992) is tested on q-state Potts models in dimensions D = 2 and 3. Our Monte Carlo data clearly distinguish between first- and second-order phase…
Validity of the single parameter scaling (SPS) in one dimensional Anderson model with purely off-diagonal disorder is being studied. It is shown that the localized region with standard symmetry is divided into two regimes: SPS and non-SPS.…
Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside…
This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit…