Joint estimation of Ising model parameters with Hamiltonian constraint

Abstract

We propose a new method for the joint estimation of parameters of the 2D Ising model. Our estimation method is the solution to the constrained optimization problem in which the objective function is a pseudo-log-likelihood and the constraint is the Hamiltonian of the external field. We used a series of Monte Carlo simulations with different shapes and sizes of our models to evaluate the behavior of a method without a Hamiltonian constraint and a method with it. We observe that both methods remain consistent with an increased number of parameters and our estimation method tends to deliver a lower variance across all model shapes and sizes compared to a simple pseudo-maximum likelihood.