scholarly journals FRG analysis of a multi-matrix model for 3d Lorentzian quantum gravity

2020 ◽  
Author(s):  
Andreas G. A. Pithis ◽  
Antonio Duarte Pereira ◽  
Astrid Eichhorn
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Recent Progress ◽  
Gravity Models ◽  
Group Method ◽  
Critical Properties ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Tensor Models ◽  
Practical Tool

At criticality, discrete quantum gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional Renormalization Group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with ABAB-interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality.

scholarly journals The phase diagram of the multi-matrix model with ABAB interaction from functional renormalization

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Astrid Eichhorn ◽  
Antonio D. Pereira ◽  
Andreas G. A. Pithis
Keyword(s):  
Phase Diagram ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Gravity Models ◽  
Group Method ◽  
Critical Properties ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Tensor Models ◽  
Practical Tool

Abstract At criticality, discrete quantum-gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional renormalization group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with ABAB interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality and subjecting the technique to another strong test of its performance in discrete quantum gravity by comparing to known results.

scholarly journals New applications of the renormalization group method in physics: a brief introduction

2011 ◽  
Vol 369 (1946) ◽  
pp. 2602-2611 ◽  
Author(s):  
Y. Meurice ◽  
R. Perry ◽  
S.-W. Tsai
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Dynamical Systems ◽  
Particle Physics ◽  
Recent Progress ◽  
Condensed Matter ◽  
Group Method ◽  
Renormalization Group Method ◽  
Theme Issue ◽  
New Applications

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

AN EMPIRICAL FORMULA FOR Q STATE POTTS MODEL IN D DIMENSIONS

1994 ◽  
Vol 08 (17) ◽  
pp. 1059-1064
Author(s):  
C. Y. PAN
Keyword(s):  
Renormalization Group ◽  
Critical Points ◽  
Potts Model ◽  
Critical Exponents ◽  
Empirical Formula ◽  
Group Method ◽  
Critical Properties ◽  
Renormalization Group Method ◽  
Primary Reference ◽  
Good Agreement

Based upon the known results of the critical properties of the q state Potts ferromagnets obtained by different methods, we proposed an empirical formula of the model. It gives the critical points and the critical exponents for general Potts spin value q in any d dimensions which are in good agreement with all the available results. It improves the results given by Migdal–Kadanoff renormalization group method. It gives more accurate results than Hajdukovic conjecture to the problem of interest. This empirical formula may serve as the primary reference to the problem of interest.

scholarly journals INVARIANT FORMULATION OF THE FUNCTIONAL RENORMALIZATION GROUP METHOD FOR U(n)×U(n) SYMMETRIC MATRIX MODELS

2012 ◽  
Vol 27 (36) ◽  
pp. 1250212 ◽  
Author(s):  
A. PATKÓS
Keyword(s):  
Renormalization Group ◽  
Symmetric Matrix ◽  
The Other ◽  
Group Method ◽  
Renormalization Group Method ◽  
Potential Approximation ◽  
Functional Renormalization Group ◽  
Local Potential Approximation ◽  
Invariant Formulation ◽  
Symmetric Theory

The Local Potential Approximation (LPA) to the Wetterich-equation is formulated explicitly in terms of operators, which are invariant under the U (n)× U (n) symmetry group. Complete formulas are presented for the two-flavor ( U (2)× U (2)) case. The same approach leads to a unique natural truncation of the functional driving the renormalization flow of the potential of the three-flavor case ( U (3)× U (3)). The procedure applied to the SU (3)× SU (3) symmetric theory, results in an equation, which potentially allows an RG-investigation of the effect of the 't Hooft term representing the U A(1) anomaly, disentangled from the other operators.

scholarly journals Optimized regulator for the quantized anharmonic oscillator

2015 ◽  
Vol 30 (12) ◽  
pp. 1550058 ◽  
Author(s):  
J. Kovacs ◽  
S. Nagy ◽  
K. Sailer
Keyword(s):  
Renormalization Group ◽  
Ground State ◽  
Evolution Equations ◽  
Energy Gap ◽  
Anharmonic Oscillator ◽  
Group Method ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
First Excited State ◽  
Symmetric Phase

The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used which includes various types of regulators as limiting cases. It was found that the value of the energy gap depends on the regulator parameters. We argue that the optimization based on the disappearance of the false, broken symmetric phase of the model leads to the Litim's regulator. The least sensitivity on the regulator parameters leads, however, to an IR regulator being somewhat different of the Litim's one, but it can be described as a perturbatively improved, or generalized Litim's regulator and provides analytic evolution equations, too.

COUNTING STATISTICS OF NONEQUILIBRIUM TUNNELING PROCESS USING FUNCTIONAL RENORMALIZATION GROUP

2010 ◽  
Vol 24 (05) ◽  
pp. 575-585 ◽  
Author(s):  
QING-QIANG XU ◽  
BEN-LING GAO ◽  
SHI-JIE XIONG
Keyword(s):  
Renormalization Group ◽  
Charge Transfer ◽  
Quantum Dot ◽  
Group Method ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Nonequilibrium Transport ◽  
Cumulant Generating Function ◽  
Full Counting Statistics ◽  
Counting Statistics

We develop a scheme to investigate the flux of nonequilibrium transport based on the full counting statistics and nonequilibrium functional renormalization group method. As an illustrative example, we study the charge transfer in the system of an interacting quantum dot connected to two noninteracting reservoirs via tunneling. Within the lowest approximation in functional renormalization group, we obtain the cumulant generating function analytically.

Sign in / Sign up

Export Citation Format

Share Document