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Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry
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10.1063/1.4771973
/content/aip/journal/jcp/138/12/10.1063/1.4771973
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4771973

Figures

Image of FIG. 1.
FIG. 1.

Cartoon of the sandwich geometry. In the ‘parallel” (or αα) setup (top) both frozen walls are taken from the same equilibrium configuration, while in the “anti-parallel” (αβ) case, they come from different configurations (bottom).

Image of FIG. 2.
FIG. 2.

Overlap at the center of the sandwich vs. sandwich half-width d in the parallel setup for (from left to right) T = 0.482, 0.350, 0.246, 0.202. Lines are exponential or compressed-exponential fits (see text). (Inset) Same data in semilog plot.

Image of FIG. 3.
FIG. 3.

Overlap in the parallel setup as a function of z for a sandwich of half-width d = 4 at several temperatures. The free region is wide enough that the overlap can reach its bulk value q 0 near the center.

Image of FIG. 4.
FIG. 4.

Overlap vs. dz (distance from wall) at fixed d (same data as Fig. 3 ) with pure exponential fits. (Inset) Same data in semilog scale.

Image of FIG. 5.
FIG. 5.

Overlap at center vs. sandwich half-width d at T = 0.203 and two values of L.

Image of FIG. 6.
FIG. 6.

Excess energy per mobile particle at T = 0.246 and several values of d, together with the bulk (PBC) average value.

Image of FIG. 7.
FIG. 7.

Excess energy vs. d at several temperatures and L = 16. Lines are exponential fits. (Inset) Same data in semilog scale.

Image of FIG. 8.
FIG. 8.

Penetration length λ vs. point-to-set correlation length ξ.

Image of FIG. 9.
FIG. 9.

Energy decay length l vs. point-to-set correlation length ξ.

Image of FIG. 10.
FIG. 10.

Energy decay length vs. two-spin correlation length for the Ising model in the square lattice. Data are from Monte Carlo simulations on a 100 × 100 lattice with single-flip Metropolis dynamics performed above the critical point, at temperatures T = 2.5J, T = 2.4J, T = 2.35J and T = 2.32J, where J is the Ising coupling constant (the critical point is T c ≈ 2.269J). The correlation length was obtained from a fit of the spin-spin space correlation function C(r) = ⟨S(0)S(r)⟩. To determine the length l, sandwich configurations were prepared as explained for the liquid case, measuring the excess energy ΔE(d) = E αβE αα for d = 1, 2, 3, 4, 5, 7.5, 10, 15, 20, 25 and 45 lattice spacings, and fitting to an exponential decay.

Tables

Generic image for table
Table I.

Point-to-set correlation length ξ, and anomaly exponent ζ, from a fit of Eq. (19) ; penetration length λ, from a fit of Eq. (20) ; and excess energy decay lengthscale l, from a fit of Eq. (21) . At the highest temperature the value of l has large uncertainty as we have very few nonzero values of ΔE.

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/content/aip/journal/jcp/138/12/10.1063/1.4771973
2013-01-02
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4771973
10.1063/1.4771973
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