A subset S of the vertex set V(G) of a weighted undirected graph G determines a cut of the graph G into S and its complementary subset G\S. The size of the cut is the sum of the weights of the edges between S and G\S. A maximum cut size is at least the size of any other cut, varying S.

For the Ising model without an external field on a graph G, the Hamiltonian becomes the following sum over the graph edges