A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

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 specialpurpose 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.spin glasses | fluctuation-dissipation relation | glasses | statics-dynamics equivalence | out-of-equilibrium dynamics T heory and experiment follow apparently diverging paths when studying the glass transition. On the one hand, experimental glass formers (spin glasses, fragile molecular glasses, polymers, colloids, and . . .) undergo a dramatic increase of characteristic times when cooled down to their glass temperature, Tg (1). Below Tg, the glass is always out of equilibrium and "aging" appears (2). Consider a rapid quench from a high temperature to the working temperature T (T < Tg), where the system is left to equilibrate for time tw and probed at a later time t + tw. Response functions such as the magnetic susceptibility turn out to depend on t/t µ w , with µ ≈ 1 (2-4). The age of the glass, tw, remains the relevant time scale even for tw as large as several days. Relating the aging experimental responses to equilibrium properties is an open problem.A promising way to fill the gap is to establish a statics-dynamics dictionary (SDD) (5-8): nonequilibrium properties at "finite times" t, tw, as obtained on samples of macroscopic size L → ∞, are quantitatively matched to equilibrium quantities computed on systems of "finite size" L [the SDD is an L ↔ (t, tw) correspondence]. Clearly, in order for it to be of any value, an SDD cannot strongly depend on the particular pair of aging and equilibrium quantities that are matched.Some time ago, we proposed one such a SDD (6-8). However, this SDD was unsatisfactory in two respects. First, L was matched only to tw (irrespectively of the probing time t + tw). Second, our SDD matched spatial correlation functions whose experimental study is only incipient (9, 10).One could think (5) of building an SDD through the generalized fluctuation-dissipation relations (GFDRs) first introduced in ref. 11 (for related developments, see refs. 12-19). The GFDRs are correct at very large times. However, on time scales that can be investigated in experiments, glassy systems are not fully thermalized because the approach to equilibrium is very slow. Strong corrections pollute GFDRs at finite times. SignificanceThe unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, etc.) is a sluggish dynamics at low temperatures. Indeed, their dynamics are so slow that thermal equilibrium is n...

Aging Rate of Spin Glasses from Simulations Matches Experiments

“…A key development has been the introduction of the Janus [10,11] and Janus II [12] computers, which have extended the numerical exploration of the dynamics almost to the experimental scale [8,13]. In addition, the introduction of quantitative statics-dynamics dictionaries (first based on microscopic quantities [8,14,15] and more recently on experimentally measurable features [13]) has clarified the relevance of the equilibrium phase for the off-equilibrium dynamics and showed how to extrapolate simulations to the experimental scale. Finally, the (macroscopic) experimental measurement of the size of glassy domains was shown to be consistent with the (microscopic) definition based on correlation functions [16].…”

“…. As in recent work [13,16,22,26] we use k = 1 (see [27] for technical details). The resulting ξ 12 is plotted in Fig.…”

Matching Microscopic and Macroscopic Responses in Glasses

“…This matching is likely to be strongly dependent on the material under consideration. We describe succinctly our simulation protocol (for details see the analysis of the aging linear response in [38]). We consider a large system (with L = 80 or 160, large enough to avoid relevant finite-size effects).…”

“…The time growth of the correlation length ξmic, as obtained from the microscopic correlation function C4(r, tw) [10,11,38], is compared to the length ξmac obtained from a fit linear in H 2 , see Eq. (7).…”

Dimensional crossover in the aging dynamics of spin glasses in a film geometry

“…In the lab, spin-glass samples are permanently out of equilibrium when studied at temperatures below the critical one, T c , implying that the equilibrium theory is not always sufficient. A possible approach to overcome this difficulty is extracting from the non-equilibrium dynamics crucial information about the (so difficult to reach) equilibrium regime [4][5][6][7]. However, custom-built computers [8] and other simulation advances [9,10] have made it possible to study theoretically [11][12][13][14][15][16][17] the simplest experimental protocol.…”