Abstract
In the presented article we present an algorithm for the computation of ground state spin configurations for the 2 d 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 2 d systems, e.g. lattice graphs with up to N = 384 × 384 spins, can be analyzed very fast. Here, we investigate the critical behavior of the corresponding 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.
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