A dedicated algorithm for calculating ground states for the triangular random bond Ising model
In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state problem can be mapped to an auxiliary minimum-weight perfect matching problem, solvable in polynomial time. Consequently, the ground state properties as well as minimum-energy domain wall (MEDW) excitations for very large 2d  systems, e.g. lattice graphs with up to N=384384 N = 384  384 spins, can be analyzed very fast. Here, we investigate the critical behavior of the corresponding T=0 T = 0 ferromagnet to spin-glass transition, signaled by a breakdown of the magnetization, using finite-size scaling analyses of the magnetization and MEDW excitation energy and we contrast our numerical results with previous simulations and presumably exact results.
random bond ising model negative-weight percolation groundstate phase transitions