## An interior point cutting plane algorithm for Ising spin glass problems

### John Mitchell

An interior point cutting plane algorithm for solving Maximum Cut problems of a particular structure is described. The problem of interest is determining the ground states of two dimensional $\pm J$ Ising spin glasses on square lattices with nearest neighbour interactions and periodic boundary conditions. Computational results for grids of sizes up to $100\times100$ are presented. An estimate of the ground state energy of an infinite spin glass system with the proportion of negative bonds equal to $0.5$ is given.

Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, July 15, 1997.

Contact: mitchj@rpi.edu