Multi-core Computation of Transfer Matrices for Strip Lattices in the Potts Model

The transfer-matrix technique is a convenient way for studying strip lattices in the Potts model since the computational costs depend just on the periodic part of the lattice and not on the whole. However, even when the cost is reduced, the transfer-matrix technique is still an NP-hard problem since the time T (|V |, |E|) needed to compute the matrix grows exponentially as a function of the graph width. In this work, we present a parallel transfer-matrix implementation that scales performance under multi-core architectures. The construction of the matrix is based on several repetitions of the deletion-contraction technique, allowing parallelism suitable to multi-core machines. Our experimental results show that the multi-core implementation achieves speedups of 3.7X with p = 4 processors and 5.7X with p = 8. The efficiency of the implementation lies between 60% and 95%, achieving the best balance of speedup and efficiency at p = 4 processors for actual multi-core architectures. The algorithm also takes advantage of the lattice symmetry, making the transfer matrix computation to run up to 2X faster than its non-symmetric counterpart and use up to a quarter of the original space.