Statistical mechanics of coupled supercooled liquids in finite dimensions

Abstract

We study the statistical mechanics of supercooled liquids when the system evolves at a temperature TT with a field \epsilonϵ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature T_0T0. We use mean-field theory to fully characterize the influence of the reference temperature T_0T0, and we mainly study the case of a fixed, low-T_0T0 value in computer simulations. We numerically investigate the extended phase diagram in the (\epsilon,T)(ϵ,T) plane of model glass-forming liquids in spatial dimensions d=2d=2 and d=3d=3, relying on umbrella sampling and reweighting techniques. For both 2d2d and 3d3d cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero \epsilonϵ ending in a critical point in the universality class of the random-field Ising model (RFIM) in d=3d=3. In d=2d=2 instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature T_gTg. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between 2d2d and 3d3d glass-formers.

Is glass a state of matter?

“…( 2) based on large deviations techniques have been proposed [34] and combined with enhanced sampling techniques [35]. As a result, the Landau free energy V (Q) has been measured in several numerical models of glass-forming liquids in dimension d = 2 and d = 3 down to very low temperatures [19,34,36,37]. The expected behaviour for V (Q) has been confirmed directly in these computer simulations, as illustrated in Fig.…”

“…This is because the lower critical dimension [9] of the random-field Ising model is d = 2, so that for d ≤ 2 there is no longer a finite transition temperature in this model [42]. This non-trivial prediction was recently confirmed in computer simulations of a two-dimensional glass-forming model [19].…”

“…Glass metastability can be established even more clearly by coupling the overlap Q to its conjugate field [19,34,36,38,39]. In three dimensions, one finds a discontinuous jump of the overlap as is increased at constant T beyond a critical value * (T ), see Fig.…”

“…Overlap order parameter Q of the liquid-glass transition. It quantifies the degree of similarity between the density profiles of two independent equilibrium configurations (here obtained from numerical simulations of a twodimensional glass-forming liquid [19]). For T > TK, the liquid explores a large number of equilibrium structures and Q 0.…”

Computer simulations of the glass transition and glassy materials

“…Contrary to random pinning, it is possible to prepare a large number of independent stable configurations at a given state point, which then paves the way for the analysis of structural [109][110][111], thermodynamic [112,113], mechanical [114,115] and transport [116] properties of supercooled liquids and glasses. Direct tests of theories of the glass transition can be performed in the experimentally relevant temperature regime [117][118][119][120], as well as exploration of excitations [121,122], and defects [123][124][125] characterising low-lying states in the potential energy landscape of glassy systems. The swap Monte Carlo algorithm then inspired novel ways to produce zero-temperature amorphous particle packings with original physical properties [126,127], and was used to understand the peculiar physical properties of ultrastable systems prepared via physical vapor deposition [128][129][130].…”