The Experts below are selected from a list of 41964 Experts worldwide ranked by ideXlab platform
Nicolás Wschebor - One of the best experts on this subject based on the ideXlab platform.
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Scale Invariance implies conformal Invariance for the three-dimensional Ising model
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension −1 exists, then Scale Invariance implies conformal Invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that Scale Invariance implies conformal Invariance for the three-dimensional Ising model.
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Scale Invariance implies conformal Invariance for the three dimensional ising model
Physical Review E, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension -1 exists, then Scale Invariance implies conformal Invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that Scale Invariance implies conformal Invariance for the three-dimensional Ising model.
Didier Sornette - One of the best experts on this subject based on the ideXlab platform.
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Discrete Scale Invariance in growing networks
2014Co-Authors: Wei Chen, Didier Sornette, Malte Schröder, Raissa M. D'souza, Jan NaglerAbstract:Discrete Scale Invariance (DSI) arises in systems where the usual (continuous) Scale Invariance (for example at phase transitions) is partially broken, leading to a remarkable discrete hierarchy of resonances in the system order parameter. DSI has broad technical, physical and biological relevance, penetrating statistical physics (Potts model, Singularities), hydrodynamics, turbulence, astronomy, evolution, fracture and economics. (D. Sornette, Phys. Rep. 297, 239 (1998)). A hierarchy of discrete micro-transitions leading up to the transition to global connectivity in models of continuous and discontinuous percolation is observed. These transitions can in some cases be observed in the relative variance of the size of the largest cluster even in the thermodynamic limit. Depending on the model these cascades exhibit either genuine discrete Scale-Invariance or a generalized (novel) form. In contrast to average values, the size of the largest cluster before the phase transition is limited to integer values. This leads to a family of scaling relations that describe the behavior of the micro-transition cascade (Chen, Schroder, D'Souza, Sornette, Nagler (under review)). Our ndings open up the possibility for the prediction of tipping in complex systems that are dominated by large-Scale disorder.
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Discrete Scale Invariance and complex dimensions
Physics Reports, 1998Co-Authors: Didier SornetteAbstract:We discuss the concept of discrete Scale Invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group equations in the seventies, complex exponents have been studied in the eighties in relation to various problems of physics embedded in hierarchical systems. Only recently has it been realized that discrete Scale Invariance and its associated complex exponents may appear ``spontaneously'' in euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples are diffusion-limited-aggregation clusters, rupture in heterogeneous systems, earthquakes, animals (a generalization of percolation) among many other systems. We review the known mechanisms for the spontaneous generation of discrete Scale Invariance and provide an extensive list of situations where complex exponents have been found. This is done in order to provide a basis for a better fundamental understanding of discrete Scale Invariance. The main motivation to study discrete Scale Invariance and its signatures is that it provides new insights in the underlying mechanisms of Scale Invariance. It may also be very interesting for prediction purposes.
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discrete Scale Invariance and complex dimensions
Physics Reports, 1998Co-Authors: Didier SornetteAbstract:Abstract We discuss the concept of discrete-Scale Invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group equations in the 1970s, complex exponents have been studied in the 1980s in relation to various problems of physics embedded in hierarchical systems. Only recently has it been realized that discrete-Scale Invariance and its associated complex exponents may appear “spontaneously” in Euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples are diffusion-limited-aggregation clusters, rupture in heterogeneous systems, earthquakes, animals (a generalization of percolation) among many other systems. We review the known mechanisms for the spontaneous generation of discrete-Scale Invariance and provide an extensive list of situations where complex exponents have been found. This is done in order to provide a basis for a better fundamental understanding of discrete-Scale Invariance. The main motivation to study discrete-Scale Invariance and its signatures is that it provides new insights in the underlying mechanisms of Scale Invariance. It may also be very interesting for prediction purposes.
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Scale Invariance and Beyond Les Houches Workshop, March 10–14, 1997
1997Co-Authors: B. Dubrulle, F. Graner, Didier SornetteAbstract:Lecture 1 Scale Invariance Without Mechanism? -- Lecture 2 Scale Invariance and Beyond: What Can We Learn from Wavelet Analysis? -- Lecture 3 Fractional Derivatives in Static and Dynamic Scaling -- Lecture 4 Multi-Dimensional Self-Similarity, and Self-Gravitating N-Body Systems -- Lecture 5 Scaling in Stock Market Data: Stable Laws and Beyond -- Lecture 6 Hysteresis, Avalanches, and Barkhausen Noise -- Lecture 7 Burgers Turbulence and the Energy Landscape of Randomly Pinned Objects -- Lecture 8 Power Laws and Scale Invariance in Physical Metallurgy -- Lecture 9 Scale Invariance in Fluids with Anticorrelated Entropy-Specific Volume Fluctuations -- Lecture 10 Scale Invariance(s) in the Cosmic Matter Distribution? -- Lecture 11 Scale Invariance of the Avalanche Effect in Phase Transition Modulated Mantle Mixing -- Lecture 12 Scale Invariance of Earthquakes -- Lecture 13 Models for Evolution and Extinction -- Lecture 14 Scale Invariance in Economics and in Finance -- Lecture 15 Models of Artificial Foreign Exchange Markets -- Lecture 16 From Scale-Invariance to Scale-Covariance in Out-of-Equilibrium Systems -- Lecture 17 Turbulence: Statistical Approach -- Lecture 18 Discrete Scale Invariance -- Lecture 19 Scale Relativity -- Lecture 20 Scaling in Turbulent Flows -- Lecture 21 Statistical Scale Symmetry Breaking.
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Discrete Scale Invariance
Scale Invariance and Beyond, 1997Co-Authors: Didier SornetteAbstract:In a nutshell, continuous Scale Invariance means reproducing itself on different time or space Scales. More precisely, an observable O which depends on a “control” parameter x is Scale invariant under the arbitrary change x →λx (1) if there is a number μ(λ) such that $$O(x) = \mu O(\lambda x)$$ (1)
Pascal Monceau - One of the best experts on this subject based on the ideXlab platform.
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Effects of deterministic and random discrete Scale Invariance on spin wave spectra
Physica E-low-dimensional Systems & Nanostructures, 2012Co-Authors: Pascal Monceau, Jean-claude Serge LévyAbstract:The properties of magnon spectra in low dimensional random Sierpinski fractals, deterministic fractals, and percolation clusters are calculated and compared. While deterministic Scale Invariance leads to singular continuous spectra with gaps and degenerated levels, random Scale Invariance leads to continuous density of states which enables to define low frequency exponents; the exponents associated to random percolation clusters and to Sierpinski fractals are significantly different, even if their fractal dimensions are very close. The study of spacing levels shows quantitatively that the degeneracy is linked to geometrical symmetry in deterministic fractals while it is strongly reduced by random discrete Scale Invariance.
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Effects of deterministic and random discrete Scale Invariance on spin wave spectra
Physica E: Low-dimensional Systems and Nanostructures, 2012Co-Authors: Pascal Monceau, Jean-claude S. LevyAbstract:International audienceThe properties of magnon spectra in low dimensional random Sierpinski fractals, deterministic fractals, and percolation clusters are calculated and compared. While deterministic Scale Invariance leads to singular continuous spectra with gaps and degenerated levels, random Scale Invariance leads to continuous density of states which enables to define low frequency exponents; the exponents associated to random percolation clusters and to Sierpinski fractals are significantly different, even if their fractal dimensions are very close. The study of spacing levels shows quantitatively that the degeneracy is linked to geometrical symmetry in deterministic fractals while it is strongly reduced by random discrete Scale Invariance
Bertrand Delamotte - One of the best experts on this subject based on the ideXlab platform.
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Scale Invariance implies conformal Invariance for the three-dimensional Ising model
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension −1 exists, then Scale Invariance implies conformal Invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that Scale Invariance implies conformal Invariance for the three-dimensional Ising model.
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Scale Invariance implies conformal Invariance for the three dimensional ising model
Physical Review E, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension -1 exists, then Scale Invariance implies conformal Invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that Scale Invariance implies conformal Invariance for the three-dimensional Ising model.
Jean-claude Serge Lévy - One of the best experts on this subject based on the ideXlab platform.
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Effects of deterministic and random discrete Scale Invariance on spin wave spectra
Physica E-low-dimensional Systems & Nanostructures, 2012Co-Authors: Pascal Monceau, Jean-claude Serge LévyAbstract:The properties of magnon spectra in low dimensional random Sierpinski fractals, deterministic fractals, and percolation clusters are calculated and compared. While deterministic Scale Invariance leads to singular continuous spectra with gaps and degenerated levels, random Scale Invariance leads to continuous density of states which enables to define low frequency exponents; the exponents associated to random percolation clusters and to Sierpinski fractals are significantly different, even if their fractal dimensions are very close. The study of spacing levels shows quantitatively that the degeneracy is linked to geometrical symmetry in deterministic fractals while it is strongly reduced by random discrete Scale Invariance.
