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Baity-Jesi M, Calore E, Cruz A, Fernandez LA, Gil-Narvión JM, Gordillo-Guerrero A, Iñiguez D, Maiorano A, Marinari E, Martin-Mayor V, Monforte-Garcia J, Muñoz Sudupe A, Navarro D, Parisi G, Perez-Gaviro S, Ricci-Tersenghi F, Ruiz-Lorenzo JJ, Schifano SF, Seoane B, Tarancón A, Tripiccione R, Yllanes D. A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements. Proc Natl Acad Sci U S A 2017; 114:1838-1843. [PMID: 28174274 PMCID: PMC5338409 DOI: 10.1073/pnas.1621242114] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We have performed a very accurate computation of the nonequilibrium fluctuation-dissipation ratio for the 3D Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.
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Affiliation(s)
- Marco Baity-Jesi
- Institut de Physique Théorique, Direction de la Recherche Fondamentale, Commissariat à L'énergie Atomique et aux Énergies Alternatives, Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Enrico Calore
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara e Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Ferrara, I-44122 Ferrara, Italy
| | - Andres Cruz
- Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
| | - Luis Antonio Fernandez
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | | | - Antonio Gordillo-Guerrero
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Ingeniería Eléctrica, Electrónica y Automática, Universidad de Extremadura, 10071, Cáceres, Spain
| | - David Iñiguez
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Fundación Agencia Aragonesa para la Investigación y Desarrollo, Diputación General de Aragón, 50003 Zaragoza, Spain
| | - Andrea Maiorano
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
- Nanotec-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
| | - Victor Martin-Mayor
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | | | - Antonio Muñoz Sudupe
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | - Denis Navarro
- Departamento de Ingeniería, Electrónica y Comunicaciones and I3A, Universidad de Zaragoza, 50018 Zaragoza, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy;
- Nanotec-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
| | - Sergio Perez-Gaviro
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Centro Universitario de la Defensa, 50090 Zaragoza, Spain
| | - Federico Ricci-Tersenghi
- Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
- Nanotec-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
| | - Juan Jesus Ruiz-Lorenzo
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Institut de Physique Théorique, Direction de la Recherche Fondamentale, Commissariat à L'énergie Atomique et aux Énergies Alternatives, Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Sebastiano Fabio Schifano
- Dipartimento di Matematica e Informatica, Università di Ferrara e INFN, Sezione di Ferrara, I-44122 Ferrara, Italy
| | - Beatriz Seoane
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain;
- Laboratoire de Physique Théorique, École Normale Supérieure, Université de Recherche Paris Sciences et Lettres, Pierre et Marie Curie, Sorbonne Universités, UMR 8549 CNRS, 75005 Paris, France
| | - Alfonso Tarancón
- Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
| | - Raffaele Tripiccione
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara e Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Ferrara, I-44122 Ferrara, Italy
| | - David Yllanes
- Instituto de Biocomputación y Física de Sistemas Complejos, 50009 Zaragoza, Spain
- Department of Physics and Soft Matter Program, Syracuse University, Syracuse, NY 13244
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Sibani P, Kenning GG. Origin of end-of-aging and subaging scaling behavior in glassy dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011108. [PMID: 20365324 DOI: 10.1103/physreve.81.011108] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2009] [Revised: 10/11/2009] [Indexed: 05/29/2023]
Abstract
Linear response functions of aging systems are routinely interpreted using the scaling variable t(obs)/t(w)(mu), where t(w) is the time at which the field conjugated to the response is turned on or off, and where t(obs) is the "observation" time elapsed from the field change. The response curve obtained for different values of t(w) are usually collapsed using values of mu slightly below one, a scaling behavior generally known as subaging. Recent spin glass thermoremanent magnetization experiments have shown that the value of mu is strongly affected by the form of the initial cooling protocol [G. F. Rodriguez, Phys. Rev. Lett. 91, 037203 (2003)], and even more importantly [G. G. Kenning, Phys. Rev. Lett. 97, 057201 (2006)], that the t(w) dependence of the response curves vanishes altogether in the limit t(obs)>>t(w). The latter result shows that t(obs)/t(w)(mu) scaling of linear response data cannot be generally valid, thereby casting some doubt on the theoretical significance of the exponent mu . In this work, a common mechanism is proposed for the origin of both subaging and end of aging behavior in glassy dynamics. The mechanism combines real and configuration space properties of the state produced by the initial thermal quench which initiates the aging process.
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Affiliation(s)
- Paolo Sibani
- Institut for Fysik og Kemi, SDU, DK5230 Odense M, Denmark.
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Abstract
We numerically analyze the statistics of the heat flow between an aging system and its thermal bath, following a method proposed and tested for a spin-glass model in a recent paper [P. Sibani and H. J. Jensen, Europhys. Lett. 69, 563 (2005)]. The present system, which lacks quenched randomness, consists of Ising spins located on a cubic lattice, with each plaquette contributing to the total energy the product of the four spins located at its corners. Similarly to our previous findings, energy leaves the system in rare but large, so-called intermittent, bursts which are embedded in reversible and equilibriumlike fluctuations of zero average. The intermittent bursts, or quakes, dissipate the excess energy trapped in the initial state at a rate which falls off with the inverse of the age. This strongly heterogeneous dynamical picture is explained using the idea that quakes are triggered by energy fluctuations of record size, which occur independently within a number of thermalized domains. From the temperature dependence of the width of the reversible heat fluctuations we surmise that these domains have an exponential density of states. Finally, we show that the heat flow consists of a temperature independent term and a term with an Arrhenius temperature dependence. Microscopic dynamical and structural information can thus be extracted from numerical intermittency data. This type of analysis seems now within the reach of time resolved microcalorimetry techniques.
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Affiliation(s)
- Paolo Sibani
- Institut for Fysik og Kemi, SDU, DK5230 Odense M, Denmark
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Kenning GG, Rodriguez GF, Orbach R. End of aging in a complex system. PHYSICAL REVIEW LETTERS 2006; 97:057201. [PMID: 17026136 DOI: 10.1103/physrevlett.97.057201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Indexed: 05/12/2023]
Abstract
Aging phenomena in complex systems have been used as an important tool to investigate the physics of complexity. In particular, aging effects in spin glasses, measured using the thermoremanent magnetization decays, have been instrumental as a probe of complex equilibrium and nonequilibrium dynamics. In this Letter, we show that aging found in spin glass materials has a finite lifetime. After the aging part of the decay has ended, we find a post-aging decay which is apparently logarithmic in nature. This decay is independent of the waiting time and part of the same mechanism that produces aging.
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Affiliation(s)
- G G Kenning
- Department of Physics, Indiana University of Pennsylvania, Indiana, PA 15705-1098, USA
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Newman CM, Stein DL. Metastable states in spin glasses and disordered ferromagnets. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5244-60. [PMID: 11970394 DOI: 10.1103/physreve.60.5244] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/1999] [Indexed: 04/18/2023]
Abstract
We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical, and is based on the convergence of sigma(t), a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit sigma(infinity). The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations, and relations to thermodynamic states. For example, we show that their overlap distribution is a delta function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.
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Affiliation(s)
- C M Newman
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
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