Equivalence between two-dimensional alternating/random Ising model and   the ground state of one-dimensional alternating/random XY chain
  It is derived that the two-dimensional Ising model with alternating/random interactions and with periodic/free boundary conditions is equivalent to the ground state of the one-dimensional alternating/random XY model with the corresponding periodic/free boundary conditions. This provides an exact equivalence between a random rectangular Ising model, in which the Griffiths-McCoy phase appears, and a random XY chain. 
Kazuhiko Minami
cond-mat.stat-mech math-ph math.MP