Joint estimation of Ising model parameters with Hamiltonian constraint

Oliver Smirnov

Physica A: Statistical Mechanics and its Applications, 2024, vol. 633, issue C

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.

Keywords: Monte Carlo; Pseudo-maximum likelihood; Constrained non-linear optimization (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:633:y:2024:i:c:s0378437123009172

DOI: 10.1016/j.physa.2023.129362

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