An efficient matching algorithm applied in statistical physics

An efficient matching algorithm applied in statistical physics

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Article ID: iaor19951133
Country: Netherlands
Volume: 52
Issue: 2
Start Page Number: 139
End Page Number: 153
Publication Date: Aug 1994
Journal: Discrete Applied Mathematics
Authors: , ,
Keywords: science
Abstract:

An efficient Operational Research 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. The authors got an improved estimate for the so-called critical concentration c of antiferromagnetic bonds where 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 they obtained c<0.108. This is, so far as is known 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<c<0.108, in agreement with the estimates of other authors.

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