An efficient matching algorithm applied in statistical physics

AbstractAn 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 pc of antiferromagnetic bonds where pc 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 pc < 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 < pc < 0.108, in agreement with the estimates of other authors