Abstract
An efficient OR matching algorithm for nonbipartite graphs is applied in simulations of groundstate energies and magnetizations of two-dimensional random Ising ± 1 spin models on square L × L-lattices as considered in Solid State Physics when studying magnetic crystal systems. We got an improved estimate for the so-called critical concentration p c of antiferromagnetic bonds where p c marks the threshold at which the magnetization disappears and what is named the phase transition between ferromagnetism and paramagnetism. In particular, from a lattice of size L = 300 we obtained p c < 0.108. This is, to our knowledge, the first time that for the problem in question a lattice of this size has been treated by means of an exact matching algorithm. Moreover, the extrapolation of the simulation results for L = 10, 20, 50, 100, 200, 300 leads to 0.095 < p c < 0.108, in agreement with the estimates of other authors.
Published Version
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