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It is derived that the two-dimensional Ising model with alternating/randominteractions and with periodic/free boundary conditions is equivalent to theground state of the one-dimensional alternating/random XY model with thecorresponding periodic/free boundary conditions. This provides an exactequivalence between a random rectangular Ising model, in which theGriffiths-McCoy phase appears, and a random XY chain.

Equivalence between two-dimensional alternating/random Ising model and the ground state of one-dimensional alternating/random XY chain