An Ising model for supercooled liquids and the glass transition

Our goal is to find a fundamental foundation for the thermal and dynamic behavior associated with the liquid-glass transition.
The simplest microscopic model for a thermodynamic phase transition is the homogeneous Ising model on an infinite lattice, but heterogeneity is known to be a crucial characteristic of supercooled liquids. Therefore, we seek the minimal modifications to the Ising model that allow it to match the broadest range of features exhibited by liquids and glasses. We have extended the standard Ising model by adding: finite-size effects, a thermal distribution of interaction energies, and orthogonal constraints on the dynamics. I will describe how this “orthogonal Ising model” mimics more than twenty features found in liquids and glasses.
Then I will discuss some additional aspects of small-system thermodynamics (“nanothermodynamics”), including a novel solution to Gibbs’ paradox and why thermal equilibrium usually involves nanoscale heterogeneity.