# Where/when did the fields of Operations Research and Spin Physics or Molecular Dynamics begin to cross-pollinate?

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?

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– Tyberius
Jul 14 '20 at 18:22
• I am not sure but wasn't Hopefield one of the first few people to start take spin glass physics to other areas? Oct 28 '21 at 15:03
• +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). Oct 28 '21 at 21:01