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Fytas NG, Martín-Mayor V, Parisi G, Picco M, Sourlas N. Finite-size scaling of the random-field Ising model above the upper critical dimension. Phys Rev E 2023; 108:044146. [PMID: 37978671 DOI: 10.1103/physreve.108.044146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 10/05/2023] [Indexed: 11/19/2023]
Abstract
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of statistical physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension D=7, i.e., above its upper critical dimension D_{u}=6, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions D>D_{u}, linear length scale L should be replaced in finite-size scaling expressions by the effective scale L_{eff}=L^{D/D_{u}}. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.
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Affiliation(s)
- Nikolaos G Fytas
- Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185 Rome, Italy and INFN, Sezione di Roma I, IPCF-CNR, P.le A. Moro 2, 00185 Rome, Italy
| | - Marco Picco
- Laboratoire de Physique Théorique et Hautes Energies, UMR7589, Sorbonne Université et CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Nicolas Sourlas
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, PARIS VI) 24 rue Lhomond, 75231 Paris Cedex 05, France
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d'Auriac JCA, Iglói F. Random-bond antiferromagnetic Ising model in a field. Phys Rev E 2022; 106:034117. [PMID: 36266800 DOI: 10.1103/physreve.106.034117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
Using combinatorial optimization techniques we study the critical properties of the two- and three-dimensional Ising models with uniformly distributed random antiferromagnetic couplings (1≤J_{i}≤2) in the presence of a homogeneous longitudinal field, h, at zero temperature. In finite systems of linear size, L, we measure the average correlation function, C_{L}(ℓ,h), when the sites are either on the same sublattice, or they belong to different sublattices. The phase transition, which is of first order in the pure system, turns to mixed order in two dimensions with critical exponents 1/ν≈0.5 and η≈0.7. In three dimensions we obtain 1/ν≈0.7, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.
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Affiliation(s)
| | - Ferenc Iglói
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
- Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary
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3
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Vasilopoulos A, Fytas NG, Vatansever E, Malakis A, Weigel M. Universality in the two-dimensional dilute Baxter-Wu model. Phys Rev E 2022; 105:054143. [PMID: 35706204 DOI: 10.1103/physreve.105.054143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 05/02/2022] [Indexed: 06/15/2023]
Abstract
We study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field Δ. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of Δ and a parallelized variant of the multicanonical approach performed at constant temperature T. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram indicates that the transition belongs to the universality class of the four-state Potts model. Previous controversies with respect to the nature of the transition are discussed and attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.
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Affiliation(s)
| | - Nikolaos G Fytas
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
| | - Erol Vatansever
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
- Department of Physics, Dokuz Eylül University, TR-35160 Izmir, Turkey
| | - Anastasios Malakis
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
- Department of Physics, University of Athens, Panepistimiopolis, GR-15784 Zografou, Greece
| | - Martin Weigel
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
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Mijatović S, Jovković D, Spasojević D. Nonequilibrium athermal random-field Ising model on hexagonal lattices. Phys Rev E 2021; 103:032147. [PMID: 33862757 DOI: 10.1103/physreve.103.032147] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 03/08/2021] [Indexed: 11/07/2022]
Abstract
We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32768×32768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.
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Affiliation(s)
- Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O.B. 44, 11001 Belgrade, Serbia
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P.O.B. 162, 11000 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O.B. 44, 11001 Belgrade, Serbia
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Monfared S, Zhou T, Andrade JE, Ioannidou K, Radjaï F, Ulm FJ, Pellenq RJM. Effect of Confinement on Capillary Phase Transition in Granular Aggregates. PHYSICAL REVIEW LETTERS 2020; 125:255501. [PMID: 33416387 DOI: 10.1103/physrevlett.125.255501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Accepted: 11/16/2020] [Indexed: 06/12/2023]
Abstract
Using a 3D mean-field lattice-gas model, we analyze the effect of confinement on the nature of capillary phase transition in granular aggregates with varying disorder and their inverse porous structures obtained by interchanging particles and pores. Surprisingly, the confinement effects are found to be much less pronounced in granular aggregates as opposed to porous structures. We show that this discrepancy can be understood in terms of the surface-surface correlation length with a connected path through the fluid domain, suggesting that this length captures the true degree of confinement. We also find that the liquid-gas phase transition in these porous materials is of second order nature near capillary critical temperature, which is shown to represent a true critical temperature, i.e., independent of the degree of disorder and the nature of the solid matrix, discrete or continuous. The critical exponents estimated here from finite-size scaling analysis suggest that this transition belongs to the 3D random field Ising model universality class as hypothesized by F. Brochard and P.G. de Gennes, with the underlying random fields induced by local disorder in fluid-solid interactions.
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Affiliation(s)
- Siavash Monfared
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Tingtao Zhou
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - José E Andrade
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Katerina Ioannidou
- CNRS, University of Montpellier, LMGC, 163 rue Auguste Broussonnet F-34090 Montpellier, France
- MultiScale Material Science for Energy and Environment UMI 3466 CNRS-MIT-Aix-Marseille Université Joint Laboratory, Cambridge, Massachusetts 02139, USA
| | - Farhang Radjaï
- CNRS, University of Montpellier, LMGC, 163 rue Auguste Broussonnet F-34090 Montpellier, France
| | - Franz-Josef Ulm
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Roland J-M Pellenq
- MultiScale Material Science for Energy and Environment UMI 3466 CNRS-MIT-Aix-Marseille Université Joint Laboratory, Cambridge, Massachusetts 02139, USA
- Department of Physics, Georgetown University, Washington, D.C. 20057, USA
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Vatansever E, Vatansever ZD, Theodorakis PE, Fytas NG. Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field. Phys Rev E 2020; 102:062138. [PMID: 33466068 DOI: 10.1103/physreve.102.062138] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
Using high-precision Monte Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques, we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on a square lattice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of a pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothing of the transition to second-order with the presence of strong scaling corrections.
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Affiliation(s)
- Erol Vatansever
- Department of Physics, Dokuz Eylül University, TR-35160 Izmir, Turkey
| | | | | | - Nikolaos G Fytas
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
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Guiselin B, Berthier L, Tarjus G. Random-field Ising model criticality in a glass-forming liquid. Phys Rev E 2020; 102:042129. [PMID: 33212666 DOI: 10.1103/physreve.102.042129] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 10/07/2020] [Indexed: 11/07/2022]
Abstract
We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field Ising model (RFIM) critical point and of a first-order transition line, in agreement with recent field-theoretical approaches. The dynamics in the vicinity of this critical point resembles the peculiar activated scaling of RFIM-like systems, and the overlap autocorrelation displays a logarithmic stretching. Our study demonstrates RFIM criticality in the thermodynamic limit for a three-dimensional supercooled liquid at equilibrium.
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Affiliation(s)
- Benjamin Guiselin
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France.,Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Gilles Tarjus
- LPTMC, CNRS-UMR 7600, Sorbonne Université, F-75005 Paris, France
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Mijatović S, Branković M, Graovac S, Spasojević D. Avalanche properties in striplike ferromagnetic systems. Phys Rev E 2020; 102:022124. [PMID: 32942372 DOI: 10.1103/physreve.102.022124] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2020] [Accepted: 07/24/2020] [Indexed: 11/07/2022]
Abstract
We present numerical findings on the behavior of the athermal nonequilibrium random-field Ising model of spins at the thin striplike L_{1}×L_{2}×L_{3} cubic lattices with L_{1}<L_{2}<L_{3}. Changing of system sizes highly influences the evolution and shape of avalanches. The smallest avalanches [classified as three-dimension- (3D) like] are unaffected by the system boundaries, the larger are sandwiched between the top and bottom system faces so are 2D-like, while the largest are extended over the system lateral cross section and propagate along the length L_{3} like in 1D systems. Such a structure of avalanches causes double power-law distributions of their size, duration, and energy with larger effective critical exponent corresponding to 3D-like and smaller to 2D-like avalanches. The distributions scale with thickness L_{1} and are collapsible following the proposed scaling predictions which, together with the distributions' shape, might be important for analysis of the Barkhausen noise experimental data for striplike samples. Finally, the impact of system size on external field that triggers the largest avalanche for a given disorder is presented and discussed.
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Affiliation(s)
- Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Milica Branković
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Stefan Graovac
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
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Fytas NG, Martín-Mayor V, Parisi G, Picco M, Sourlas N. Evidence for Supersymmetry in the Random-Field Ising Model at D=5. PHYSICAL REVIEW LETTERS 2019; 122:240603. [PMID: 31322399 DOI: 10.1103/physrevlett.122.240603] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2019] [Indexed: 06/10/2023]
Abstract
We provide a nontrivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional disordered system with some other correlation functions in a D-2 clean system. We first show how to check these relationships in a finite-size scaling calculation and then perform a high-accuracy test. While the supersymmetric predictions are satisfied even to our high accuracy at D=5, they fail to describe our results at D=4.
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Affiliation(s)
- Nikolaos G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy and INFN, Sezione di Roma I, IPCF-CNR, Piazzale A. Moro 2, 00185 Rome, Italy
| | - Marco Picco
- Laboratoire de Physique Théorique et Hautes Energies, UMR7589, Sorbonne Université et CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Nicolas Sourlas
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, PARIS VI), 24 rue Lhomond, 75231 Paris Cedex 05, France
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10
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Fytas NG, Zierenberg J, Theodorakis PE, Weigel M, Janke W, Malakis A. Universality from disorder in the random-bond Blume-Capel model. Phys Rev E 2018; 97:040102. [PMID: 29758610 DOI: 10.1103/physreve.97.040102] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 01/23/2023]
Abstract
Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L^{*}≈32 for the chosen parameters.
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Affiliation(s)
- N G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - J Zierenberg
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany.,Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.,Bernstein Center for Computational Neuroscience, 37077 Göttingen, Germany
| | - P E Theodorakis
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - M Weigel
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - W Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - A Malakis
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom.,Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, GR 15784 Zografou, Greece
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Fytas NG, Martín-Mayor V, Picco M, Sourlas N. Restoration of dimensional reduction in the random-field Ising model at five dimensions. Phys Rev E 2017; 95:042117. [PMID: 28505873 DOI: 10.1103/physreve.95.042117] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Indexed: 11/07/2022]
Abstract
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.
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Affiliation(s)
- Nikolaos G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain.,Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Marco Picco
- Sorbonne Universités, Université Pierre et Marie Curie-Paris VI, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, 75252 Paris Cedex 05, France
| | - Nicolas Sourlas
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, PARIS VI) 24 rue Lhomond, 75231 Paris Cedex 05, France
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