scholarly journals Non-Gaussian fixed points of the block spin transformation. Hierarchical model approximation

1983 ◽  
Vol 89 (2) ◽  
pp. 191-220 ◽  
Author(s):  
K. Gawędzki ◽  
A. Kupiainen
Keyword(s):  
Fixed Points ◽  
Hierarchical Model ◽  
Model Approximation ◽  
Non Gaussian ◽  
Block Spin Transformation ◽  
Block Spin

scholarly journals Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 86 ◽  
Author(s):  
Vincent Lahoche ◽  
Dine Ousmane Samary
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Expansion Method ◽  
Flow Equation ◽  
Nucl Phys ◽  
Flow Equations ◽  
First Order Phase Transition ◽  
Group Field Theory ◽  
Non Gaussian

This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on the series of our three papers (Lahoche, et al., Class. Quantum Gravity 2018, 35, 19), (Lahoche, et al., Phys. Rev. D 2018, 98, 126010) and (Lahoche, et al., Nucl. Phys. B, 2019, 940, 190–213). We consider the polynomial Abelian U ( 1 ) d models without the closure constraint. More specifically, we discuss the case of the quartic melonic interaction. We present a new approach, namely the effective vertex expansion method, to solve the exact Wetterich flow equation and investigate the resulting flow equations, especially regarding the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward–Takahashi identities and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a first order phase transition into the reduced phase space given by the Ward constraint.

Unifying Laws in Multidisciplinary Power-Law Phenomena: Fixed-Point Universality and Nonextensive Entropy

2004 ◽  
Author(s):  
Alberto Robledo
Keyword(s):  
Random Walks ◽  
Fixed Points ◽  
Power Law ◽  
Nonlinear Dynamical Systems ◽  
Power Laws ◽  
Basins Of Attraction ◽  
Market Prices ◽  
Nonlinear Dynamical ◽  
Power Law Decay ◽  
Non Gaussian

Critical, power-law behavior in space and/or time manifests in a large variety of complex systems [12] within physics and, nowadays, more conspicuously in other fields, such as biology, ecology, geophysics, and economics. Universality, the same power law holding for completely different systems, is a consequence of the characteristic self-similar, scale-invariant property of criticality, and can be understood in terms of basins of attraction of the renormalization-group (RG) fixed points. However, the guiding quality of a variatkmal approach has been seemingly lacking in the theoretical studies of critical phenomena. Here we give an account of entropy extrema associated with fixed points of RG transformations. As illustrations, we consider simple one-dimensional models of random walks and nonlinear dynamical systems. In describing these systems we consider distribution and/or time relaxation functions with power-law decay that may have infinite first- or second- and higher-order moments. When these moments diverge, we observe the emergence of nonexponential or non-Gaussian fractal properties that can be measured by the nonextensive Tsallis entropy index q. We note that the presence of nonextensive properties may signal situations of hindered movement among the system's possible configurations. Some representative applications within physics, but with suggested or recognized connections to other fields, are critical behavior in fluids and magnets, anomalous diffusion processes, transitions to chaos in nonlinear systems, and relaxation properties of supercooled liquids near the glass formation. Two prototypical model systems serve to illustrate the development of critical states characterized by power laws from generic states described by exponential behavior. These are random walks and nonlinear iterated maps that we discuss below in some detail. Random walks [18] are suitable, for example, for representing Brownian motion (molecular thermal motion under the microscope), but also for many types of data originating from diverse disciplines. One type is that which comes in the form of a "time series," a temporal sequence of measured values, for instance, stock market prices in economics or electroencephalographic potentials in medicine.

scholarly journals MULTI-SPIN CODING OF THE MONTE CARLO SIMULATION OF THE THREE-STATE RANDOM POTTS MODEL AND THE BLOCK-SPIN TRANSFORMATION

1996 ◽  
Vol 06 (06) ◽  
pp. 747-763 ◽  
Author(s):  
MACOTO KIKUCHI ◽  
YUTAKA OKABE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Potts Model ◽  
Multispin Coding ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Random Mixture ◽  
Block Spin Transformation ◽  
Block Spin

The multi-spin coding of the Monte Carlo simulation of the three-state Potts model on the simple cubic lattice is presented. The ferromagnetic (F) model, the antiferromagnetic (AF) model, and the random mixture of the F and AF couplings are treated. The multispin coding technique is also applied to the block-spin transformation. The block-spin transformation of the F Potts model is simply realized by the majority rule, whereas the AF three-state Potts model is transformed to the block spin having a six-fold symmetry.

Non-Gaussian Diffusion of Phosphorus and Arsenic in Silicon with Local Density Diffusivity Model

2010 ◽  
Vol 303-304 ◽  
pp. 21-29 ◽  
Author(s):  
Frank Wirbeleit
Keyword(s):  
Local Density ◽  
Host Lattice ◽  
Model Approximation ◽  
Near Surface ◽  
Impurity Species ◽  
Surface Enhanced ◽  
Non Gaussian ◽  
The Given ◽  
Diffusion Flows ◽  
Diffusion Profiles

In the light of published phosphorus and arsenic diffusion profiles [1,2] a non-Gaussian mathematical diffusion model is developed in this work based on separate forward and reflected impurity diffusion flows and called local density diffusion (LDD) model. The LDD model includes the rational function diffusion (RFD) model published in [3] and represents an improvement for near surface and tail concentration profile slope approximation by introducing just one single empirical fit parameter “r”. This single fit parameter is related to the given combination of impurity species (phosphorus: r=0.18; arsenic: r=0.43) in the applied host lattice system (silicon), but does not vary while approximating different experiments with different impurity surface concentrations and penetration depths [1,2]. Based on the LDD approximation in this work a surface enhanced diffusivity for phosphorus and a tail decelerated diffusion for arsenic is suggested in comparison to RFD model approximation only. The local density diffusivity is found to be non-linear along the penetration path and reaches its maximum at a distance LLDD from the surface.

scholarly journals Block spin transformation on the dual lattice and monopole action

1996 ◽  
Vol 47 (1-3) ◽  
pp. 270-273 ◽  
Author(s):  
Tsuneo Suzuki ◽  
Yoshimi Matsubara ◽  
Shinji Ejiri ◽  
Kazuya Yamada ◽  
Natsuko Arasaki
Keyword(s):  
Dual Lattice ◽  
Block Spin Transformation ◽  
Block Spin
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