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Register a new userThe Gardner correlation length scale in glasses
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The Gardner length scale $xi$ is the correlation length in the vicinity of the Gardner transition, which is an avoided transition in glasses where the phase space of the glassy phase fractures into smaller sub-basins on experimental time scales. We argue that $xi$ grows like $ sim sqrt{B_{infty}/G_{infty}}$, where $B_{infty}$ is the bulk modulus and $G_{infty}$ is the shear modulus, both measured in the high-frequency limit of the glassy state. We suggest that $xi$ might be inferred from stress-stress correlation functions, which is more practical for experimental investigation than studying two copies of the system, which can only be done in numerical simulations. Our arguments are illustrated by explicit calculations for a system of disks moving in a narrow channel, which is solved exactly by transfer matrix techniques.
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We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility $chi_3^{(3)}$ from slightly below the usual glass transition temperature down to $10K$. According to the mean field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then $chi_3^{(3)}$, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature $T_G$. We find instead that upon cooling $| chi_3^{(3)} |$ decreases by several orders of magnitude and becomes roughly constant in the regime $100K-10K$. We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol.
We report on zero field cooled magnetization relaxation experiments on a concen- trated frozen ferrofluid exhibiting a low temperature superspin glass transition. With a method initially developed for spin glasses, we investigate the field dependence of the relaxations that take place after different aging times. We extract the typical number of correlated spins involved in the aging dynamics. This brings important insights into the dynamical correlation length and its time growth. Our results, consistent with expressions obtained for spin glasses, extend the generality of these behaviours to the class of superspin glasses. Since the typical flipping time is much larger for superspins than for atomic spins, our experiments probe a time regime much closer to that of numerical simulations.
Several theories of the glass transition propose that the structural relaxation time {tau}{alpha} is controlled by a growing static length scale {xi} that is determined by the free energy landscape but not by the local dynamical rules governing its exploration. We argue, based on recent simulations using particle-radius-swap dynamics, that only a modest factor in the increase in {tau}{alpha} on approach to the glass transition may stem from the growth of a static length, with a vastly larger contribution attributable instead to a slowdown of local dynamics. This reinforces arguments that we base on the observed strong coupling of particle diffusion and density fluctuations in real glasses
The growth of the spin-glass correlation length has been measured as a function of the waiting time $t_{mathrm{w}}$ on a single crystal of CuMn (6 at.%), reaching values $xisim 150$ nm, larger than any other glassy correlation-length measured to date. We find an aging rate $mathrm{d}ln,t_{mathrm{w}}/mathrm{d}ln,xi$ larger than found in previous measurements, which evinces a dynamic slowing-down as $xi$ grows. Our measured aging rate is compared with simulation results by the Janus collaboration. After critical effects are taken into account, we find excellent agreement with the Janus data.
Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.
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