The Ising Model and Computational Complexity
Finding the minimal energy configuration in the Ising model is NP-hard, and many problems can be directly reduced to it. For a list, including Karp's original 21 NP-hard problem see e.g. Ising formulations of many NP problems. The Ising model is also equivalent to unconstrained quadratic binary optimization which also can be used to model a large number of other NP-complete problems, see e.g. A unified modeling and solution framework for combinatorial optimization problems.