Abstract
For square, triangular, and for hexagonal lattices there is numerical and theoretical support that the ground-state thresholdp c between ferro- and paramagnetism in random 2D Ising ±J models, withp as the concentration of antiferromagnetic bonds, is identical top*which is characterized by minimal matching properties of frustrated plaquettes. From square lattices of size 100×100 we have got pc,sq<0.117 by simulations which produced average groundstate magnetizations per spin by means of exact minimal matchings. Moreover, from the squareL×L-lattices treated (L = 10, 20, 50, 100) we obtained the estimatep c,sq ≈0.1 which is in agreement with the Grinstein estimatep c,sq ≈0.099 andp c,sq ≈0.105 by Freund and Grassberger.
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