Related papers: Fisher Renormalization for Logarithmic Corrections
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, there is no notion of design optimality…
We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and…
We pose the converse Madelung question: not whether Fisher information can reproduce quantum mechanics, but whether it is necessary. We work with minimal, physically motivated axioms on density and phase: locality, probability conservation,…
A problem of identification of piecewise-constant unknown parameters of a linear regression equation (LRE) is considered. Such parameters change their values over the interval of the regressor finite (rather than persistent) excitation. To…
Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing…
We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their…
In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections…
In a recent paper Stevenson claimed that analysis of the data on the wave function renormalization constant near the critical point of the 4d Ising model is not consistent with analytical expectations. Here we present data with improved…
We perform numerical simulations of the lattice-animal problem at the upper critical dimension d=8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the…
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
The renormalization group method is applied to the three-loop effective potential of the massive $\phi^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit…
The renormalization group method, more specifically the Wegner-Houghton equation, is used to find first order phase transitions in a simple scalar field theory with a polynomial potential. An improved definition of the running parameters…
Quantum metrology leverages quantum effects such as squeezing, entanglement, and other quantum correlations to boost precision in parameter estimation by saturating quantum Cramer Rao bound, which can be achieved by optimizing quantum…
Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square…