title: Mean-field theory for the inverse Ising problem at low temperatures.
abstract: The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetizations and correlations), mean-field approximations are often used, allowing the determination of model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here, we show how clustering spin configurations can approximate these thermodynamic states and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.
authors.affiliation: Institute for Theoretical Physics, University of Cologne, Köln, Germany. cnguyen@thp.uni-koeln.de
authors.forename: H Chau
authors.initials: HC
authors.lastname: Nguyen
authors.forename: Johannes
authors.initials: J
authors.lastname: Berg
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D003080:Cold Temperature; D008962:Models, Theoretical; D013816:Thermodynamics