Superposition principle and nonlinear response in spin glasses
Ilaria Paga
(1)
,
Q. Zhai
(2)
,
Marco Baity-Jesi
(3)
,
Enrico Calore
(4)
,
Andrés Cruz
(5)
,
C. Cummings
(6)
,
Luis Antonio Fernandez
(7)
,
Jose Miguel Gil-Narvion
(8)
,
Isidoro Gonzalez-Adalid Pemartin
(7)
,
Antonio Gordillo-Guerrero
(9)
,
David Iñiguez
(5)
,
Gregory Kenning
(6)
,
Andrea Maiorano
(10)
,
Enzo Marinari
(11)
,
Victor Martin-Mayor
(7)
,
Javier Moreno-Gordo
(5)
,
Antonio Muñoz-Sudupe
(7)
,
Denis Navarro
(12)
,
Raymond Orbach
(13)
,
Giorgio Parisi
(11)
,
Sergio Perez-Gaviro
(5)
,
Federico Ricci-Tersenghi
(11)
,
Juan Ruiz-Lorenzo
(9)
,
Sebastiano Fabio Schifano
(4)
,
Deborah Schlagel
(14)
,
Beatriz Seoane
(15)
,
Alfonso Tarancon
(5)
,
David Yllanes
(7)
1
NANOTEC -
CNR Istituto di Nanotecnologia
2 Xjtu - Xi'an Jiaotong University
3 EAWAG - Swiss Federal Insitute of Aquatic Science and Technology [Dübendorf]
4 UniFE - Università degli Studi di Ferrara = University of Ferrara
5 Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
6 Indiana University of Pennsylvania
7 UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]
8 BIFI - Instituto de Biocomputación y Física de Sistemas Complejos = Institute for Biocomputation and Physics of Complex Systems
9 UEX - Universidad de Extremadura - University of Extremadura
10 UNISI - Università degli Studi di Siena = University of Siena
11 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
12 I3A - Aragón Institute of Engineering Research [Zaragoza]
13 University of Texas at Austin [Austin]
14 Ames Laboratory [Ames, USA]
15 TAU - TAckling the Underspecified
2 Xjtu - Xi'an Jiaotong University
3 EAWAG - Swiss Federal Insitute of Aquatic Science and Technology [Dübendorf]
4 UniFE - Università degli Studi di Ferrara = University of Ferrara
5 Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
6 Indiana University of Pennsylvania
7 UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]
8 BIFI - Instituto de Biocomputación y Física de Sistemas Complejos = Institute for Biocomputation and Physics of Complex Systems
9 UEX - Universidad de Extremadura - University of Extremadura
10 UNISI - Università degli Studi di Siena = University of Siena
11 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
12 I3A - Aragón Institute of Engineering Research [Zaragoza]
13 University of Texas at Austin [Austin]
14 Ames Laboratory [Ames, USA]
15 TAU - TAckling the Underspecified
Ilaria Paga
- Fonction : Auteur
- PersonId : 1325221
- ORCID : 0000-0002-6391-0226
Marco Baity-Jesi
- Fonction : Auteur
- PersonId : 1317585
- ORCID : 0000-0002-8723-906X
Luis Antonio Fernandez
- Fonction : Auteur
- PersonId : 1325215
- ORCID : 0000-0001-9102-7652
David Iñiguez
- Fonction : Auteur
- PersonId : 1325216
- ORCID : 0000-0003-2916-5493
Enzo Marinari
- Fonction : Auteur
- PersonId : 755069
- ORCID : 0000-0002-3464-4133
Victor Martin-Mayor
- Fonction : Auteur
- PersonId : 1325217
- ORCID : 0000-0002-3376-0327
Javier Moreno-Gordo
- Fonction : Auteur
- PersonId : 1325218
- ORCID : 0000-0002-0420-8605
Antonio Muñoz-Sudupe
- Fonction : Auteur
- PersonId : 1325219
- ORCID : 0000-0002-3613-3302
Denis Navarro
- Fonction : Auteur
- PersonId : 1325220
- ORCID : 0000-0002-0795-8743
Sergio Perez-Gaviro
- Fonction : Auteur
- PersonId : 1325222
- ORCID : 0000-0001-8425-7345
Federico Ricci-Tersenghi
- Fonction : Auteur
- PersonId : 1325758
- ORCID : 0000-0003-4970-7376
Juan Ruiz-Lorenzo
- Fonction : Auteur
- PersonId : 1325223
- ORCID : 0000-0003-0551-9891
Sebastiano Fabio Schifano
- Fonction : Auteur
- PersonId : 1325759
- ORCID : 0000-0002-0132-9196
Beatriz Seoane
- Fonction : Auteur
- PersonId : 1325175
- IdHAL : beatriz-seoane-bartolome
- ORCID : 0000-0003-4007-9406
David Yllanes
- Fonction : Auteur
- PersonId : 1325224
- ORCID : 0000-0001-7276-2942
Résumé
The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature Tr=T/Tg=0.95, where Tg is the spin-glass condensation temperature. For H>10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t,tw;H). Here, t is the time after H changes, and tw is the time from the quench for T>Tg to the working temperature T until H changes. We connect the growth of ξ(t,tw;H) to the barrier heights Δ(tw) that set the dynamics. The effect of H on the magnitude of Δ(tw) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ(tw). Superposition is preserved if Δ(tw) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap qEA and the overlap q[Δ(tw)]). However, superposition is violated if Δ(tw) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(tw) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,tw;H) slows down as ξ(t,tw;H) increases. In this paper, we display the difference between the zero-field-cooled ξZFC(t,tw;H) and the thermoremanent magnetization ξTRM(t,tw;H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.
