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Register a new userOn the Slowing Down of Spin Glass Correlation Length Growth:simulations meet experiments
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Victor Martin-Mayor
Publication date
2020
fields
Physics
and research's language is
English
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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.
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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.
Measuring ThermoRemanent Magnetization (TRM) decays on a single crystal CuMn(6$%$) spin glass sample, we have systematically mapped the rapid decrease of the characteristic timescale $tw_{eff}$ near $T_g$. Using $tw_{eff}$ to determine the length scale of the growth of correlations during the waiting time, $xi_{TRM}$, (observed in both numerical studies and experiment), we observe both growth of $xi_{TRM}$ in the spin glass phase and then a rapid reduction very close to $T_g$. We interpret this reduction in $xi_{TRM}$, for all waiting times, as being governed by the critical correlation length scale $xi_{crit}=a(T-T_c)^{- u}$.
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.
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
As a guideline for experimental tests of the ideal glass transition (Random Pinning Glass Transition, RPGT) that shall be induced in a system by randomly pinning particles, we performed first-principle computations within the Hypernetted chain approximation and numerical simulations of a Hard Sphere model of glass-former. We obtain confirmation of the expected enhancement of glassy behaviour under the procedure of random pinning, which consists in freezing a fraction $c$ of randomly chosen particles in the positions they have in an equilibrium configuration. We present the analytical phase diagram as a function of $c$ and of the packing fraction $phi$, showing a line of RPGT ending in a critical point. We also obtain first microscopic results on cooperative length-scales characterizing medium-range amorphous order in Hard Spere glasses and indirect quantitative information on a key thermodynamic quantity defined in proximity of ideal glass transitions, the amorphous surface tension. Finally, we present numerical results of pair correlation functions able to differentiate the liquid and the glass phases, as predicted by the analytic computations.
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