Conjecture on the exact transition point of the random Ising ferromagnet

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Abstract
Presents a conjecture on the exact value of the transition point of the random Ising ferromagnet on the square lattice. Only the bond problem is treated; each neighbouring pair of spins has an interaction of strength J(>or=0), where J is a random variable with an arbitrarily given probability distribution. To solve the problem an exact duality transformation and the replica method are used. In order to deduce the transition point from the duality relation only it is necessary to make an unconfirmed assumption concerning the symmetry of the distribution of singularities of the free energy.