Condensation of Helium in Aerogel and Athermal Dynamics of the Random-Field Ising Model

High resolution measurements reveal that condensation isotherms of ${}^4\mathrm{He}$ in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

Figure 1

(a) Hysteresis between adsorption and desorption isotherms at $T=4.40$ and 4.95 K. $P_{\text{sat}}(T)$ is the bulk vapor pressure. (b) Adsorption isotherms for $T=4.40$, 4.50, 4.60, 4.70, 4.80, 4.90, 4.95, and 5.06 K. $\tilde{P}(T)$ is the pressure at which the slope of the isotherm is maximum. The $y$ scale applies to the 4.40 K curve, the other curves are vertically shifted by 0.2 for clarity.

Figure 2

(a) Positions of the laser sheet and of the CCD cameras relative to the aerogel. (b) Pictures of the illuminated region (1 cm height) taken with the 135° CCD (logarithmic gray scale) at increasing liquid fractions (given above the pictures) during isotherms at $T=4.40$ and 4.95 K. The arrows show the corresponding points on the isotherms. (c) Perspective view of a 3D tomographic reconstruction (see text) close to the end of the condensation isotherm ($\mathrm{\Phi }\approx 0.95$) at 4.60 K. The bright region, i.e., the not yet filled part of the aerogel, is located in its left part.

Figure 3

Intensity scattered at 135° (from the region marked by a black rectangle on the inset picture) during condensation at the temperatures of Fig. 1. $P_0(T)$ is the pressure at which the optical signal is maximum at a given temperature. The $y$ scale applies to the 4.40 K curve, the other curves are vertically shifted by 0.2 for clarity.

Figure 4

(a) Central parts of pictures taken along a minor hysteresis loop at $T=4.60\mathrm{K}$ ($<T^{*}$). (b) Corresponding optical signal from the dot in (a) as a function of pressure. In chronological order, red (dark gray) is the initial filling; black shows partial emptying; green (light gray) is filling from the partially emptied state. (c) Hypothetical distribution of metastable states (shaded area, only shown for $P>P_D$) in the ($P$, $\phi$) plane, and paths deduced from the local optical signal in (a) and (b).