ON THE GROUND-STATE THRESHOLD IN RANDOM 2-DIMENSIONAL ISING +/- J-MODELS

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