Joint estimation of Ising model parameters with Hamiltonian constraint

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.

Automated summary

This study proposes a new method for simultaneously estimating the parameters of the 2D Ising model. The method solves a constrained optimization problem, where the objective function is a pseudo-log-likelihood and the constraint is the Hamiltonian of the external field. Monte Carlo simulations were conducted using models of different shapes and sizes to evaluate the performance of the method with and without the Hamiltonian constraint. The results demonstrate that the proposed estimation method yields lower variance across all model shapes and sizes compared to a simple pseudo-maximum likelihood.