Percolation transition in two-dimensional ±J Ising spin glasses

The percolation properties of geometrical clusters are investigated for the Ising spin glasses in the square and triangular lattices with the asymmetric weights of ferromagnetic and antiferomagnetic bonds. By Monte Carlo simulation, we obtain the phase diagram of the percolation transition temperature as a function of the weight of ferromagnetic bonds. At each transition temperature, we estimate the critical exponents ν and γ which agree well with those exponents belonging to the universality class of the random bond percolation except for the pure ferromagnetic case.