Solving the Ising model exactly on a 5×5×4 lattice using the Connection machine

Abstract

We implement a recently proposed exact method for solving distrete statistical models for the 3-dimensional Ising model with open boundary conditions. Our computations were done on the Connection machine because the problem maps very naturally onto massively parallel architectures. We explicitly calculate the number of states of the system at each energy for systems of size 5×4×L_z, for L_z≤5. On serial or vector computers, the time for the computation scales with the volume V like V2^L_λL_ν. On the Connection Machine, the calculation can be spread across the processors. This decreases the computation requirements by a factor equal to the number of processors. We describe the method, its implementation on the Connection Machine both in PARIS and in FORTRAN, and our results. We also state the requirements for solving larger systems using this method.