Recovering 0 Kelvin Effective Hamiltonian Parameters from High-Temperature Disordered Phases

Abstract

Effective Hamiltonians, when used in tandem with statistical mechanics techniques, offer a rigorous connection between 0 Kelvin ab-initio predictions and finite temperature experimental observations. For alloys, cluster expansion Hamiltonians can coarse-grain out the complex, many-body electron problem of density functional theory, yielding a series of simple site-wise basis functions (e.g., products of site occupancy variables) on an atomic scale. The resulting energy polynomial is computationally inexpensive, and hence suitable for the (tens of) thousands of calculations of large systems required by stochastic methods. We present a new method to run the statical mechanics problem "in reverse", using high-temperature observations and thermodynamic connections to construct an effective Hamiltonian and thereby predict the 0 Kelvin energy spectrum and associated ground states. By re-examining the cluster expansion formalism through the lens of entropy-maximization approaches, we develop an algorithm to select clusters and determine cluster interactions using only a few, high-temperature experiments on disordered phases. We demonstrate that our approach can recover not only the stable ground states at 0 Kelvin, but also the full phase behavior for three realistic two-dimensional and three-dimensional alloy test-cases.