Related papers: Real Space Renormalization in Statistical Mechanic…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
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…
Inspired by the idea of stochastic quantization proposed by Parisi and Wu, we construct the transition probability matrix which plays a central role in the renormalization group through a stochastic differential equation. By establishing…
In this paper, we introduce new reference observables to establish a scaling formula in the renormalization group equation. Using the transfer matrix method, we calculate the two point observables of the one dimensional Ising model without…
Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea…
Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a…
We develop a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponent $\nu$ near criticality of higher-dimensional quantum Ising and Potts models in a transverse field. Our method is…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to…
We examine the challenging problem of constructing reduced models for the long time prediction of systems where there is no timescale separation between the resolved and unresolved variables. In previous work we focused on the case where…
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…
Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…
This article considers change point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on $U$-statistic in Chen…
We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a…
A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in…
In this paper, we introduce a real-space renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization…
Real space renormalization group maps, e.g., the majority rule transformation, map Ising type models to Ising type models on a coarser lattice. We show that each coefficient of the renormalized Hamiltonian in the lattice gas variables…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…