1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Microscopic models of mode-coupling theory: The scenario
Rent:
Rent this article for
USD
10.1063/1.4746695
/content/aip/journal/jcp/137/8/10.1063/1.4746695
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/8/10.1063/1.4746695
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Phase diagram for z = 4 and facilitation as in Eq. (20). The dark region is the glassy phase. The dotted/solid line is the hybrid/continuous transition. Inset: Fraction of frozen spins, Eq. (A8), vs temperature for several values of q and r = 10−3. Below q = 1/2, Φ jumps to a finite value at the transition which is represented by the dotted line.

Image of FIG. 2.
FIG. 2.

Persistence vs time for several values of q both in the discontinuous (q = 0, 0.2, and 0.4) and the continuous region (0.52) of the phase diagram, Fig. 1, for r = 10−3 and several temperatures, either above and below . The solid black lines show the theoretical prediction, Eq. (A8), for the plateau heights for while the dotted ones signal the critical plateau at , q < 1/2. For temperatures above the transition, the long time value of the persistence is zero.

Image of FIG. 3.
FIG. 3.

Asymptotic fraction of blocked spins Φ (plateau height) as the temperature approaches for several values of r and q = 0.52 in the continuous region of the phase diagram. Points are the result of simulations while the lines are from Eq. (A8). The relevant temperature interval, in which Φ ∼ ε−1, is not accessible in our numerical simulation when r ≠ 0. Inset: The same for q = 0.2 for which the transition is discontinuous (notice the different labels in the y-axis).

Image of FIG. 4.
FIG. 4.

Data collapse of persistence data for several values of q versus the rescaled time, t/τ, where τ is the characteristic time associated with the α relaxation. We obtain a good collapse for data such that ϕ(t) < Φ c and, as Φ c → 0 when q → 1/2, the collapse region decreases as well, disappearing above the dynamical tricritical point. The collapsed region is well described by a KWW stretched exponential, shown as solid lines for q = 0 and 0.2. The stretched exponent is 0.5 for q = 0 and 0.35 for q = 0.2.

Image of FIG. 5.
FIG. 5.

Equilibrium relaxation at criticality for discontinuous () and continuous () ergodic-nonergodic transition: solid lines in the main panels are power-law fits with exponents a ≃ 0.23 and 0.31, respectively. Inset: β-relaxation time vs temperature difference . The solid lines are power-law functions with exponents 1/2a and 1/a, where the value of a is obtained by the fits in the main panel.

Image of FIG. 6.
FIG. 6.

Symmetric departure from the critical power law behavior for curves at temperatures equidistant from , for q = 0.52. The closer the temperature gets to , the more symmetrical the curves become and the longer it takes to depart from the critical power law. An analogous behavior is observed for q = 0.2 as well.

Image of FIG. 7.
FIG. 7.

Exponent a obtained from the critical relaxation (circles) and from the characteristic time as the critical line is approached from above (squares). The solid lines are power-law fits that vanish as q → 1/2, consistently with a logarithmic relaxation at that point.

Image of FIG. 8.
FIG. 8.

Estimate of the exponent b for q = 0.2 and r = 10−3. For this value of q, T c ≃ 0.58 and one obtains γ ≃ 2.81, a ≃ 0.25 and, using Eq. (7), b ≃ 0.61. This predicted value is in very good agreement with the simulation, as shown by the solid line whose slope is 0.61.

Image of FIG. 9.
FIG. 9.

Phase diagram, temperature T vs fraction of constrained spins q, for the ternary mixture 0+2+3 (and 0+2+4) on a Bethe lattice with z = 4 and facilitation as in Eq. (A10). The dotted/full lines are discontinuous/continuous liquid glass transitions for various r. The line passing through the circles is the tricritical line.

Image of FIG. 10.
FIG. 10.

Phase diagram for the ternary mixtures 0+1+2 on a Bethe lattice with z = 4 and facilitation as in Eq. (A18). The glassy region is located below the lines which represent discontinuous liquid-glass transitions for various r.

Image of FIG. 11.
FIG. 11.

Phase diagram for the ternary mixture 0+1+3 (and 0+1+4) on a Bethe lattice with z = 4 and facilitation as in Eq. (A20). The glassy region is located below the lines which represent continuous liquid-glass transitions for various r.

Loading

Article metrics loading...

/content/aip/journal/jcp/137/8/10.1063/1.4746695
2012-08-22
2014-04-19
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Microscopic models of mode-coupling theory: The F12 scenario
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/8/10.1063/1.4746695
10.1063/1.4746695
SEARCH_EXPAND_ITEM