Surprised to see an entire article about Ising model problems without any mention of the machines designed to solve them!
This is exactly the kind of problems that the D-Wave quantum computers are designed to run, and in fact simulations of physical systems are one place where we've been able to demonstrate solid progress, e.g. https://science.sciencemag.org/content/361/6398/162 and several other papers.
I'd highly encourage anyone interested in the Ising Hamiltonian and its uses for optimization problems to check out what we're doing and sign up for D-Wave Leap at www.dwavesys.com - we have demos, an in-browser IDE, Jupyter notebooks, a comprehensive Python SDK with excellent docs, and we'll give you free QPU time to run your problems in realtime on a quantum annealer.