Reconstruction of the lattice Hamiltonian models from the observations of microscopic degrees of freedom in the presence of competing interactions

The emergence of scanning probe and electron beam imaging techniques have allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descriptors in turn can be associated with the local symmetry breaking phenomena, representing stochastic manifestation of underpinning generative physical model. Here, we explore the reconstruction of exchange integrals in the Hamiltonian for the lattice model with two competing interactions from the observations of the microscopic degrees of freedom and establish the uncertainties and reliability of such analysis in a broad parameter-temperature space. As an ancillary task, we develop a machine learning approach based on histogram clustering to predict phase diagrams efficiently using a reduced descriptor space. We further demonstrate that reconstruction is possible well above the phase transition and in the regions of the parameter space when the macroscopic ground state of the system is poorly defined due to frustrated interactions. This suggests that this approach can be applied to the traditionally complex problems of condensed matter physics such as ferroelectric relaxors and morphotropic phase boundary systems, spin and cluster glasses, quantum systems once the local descriptors linked to the relevant physical behaviors are known.