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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.

preprint2012arXivOpen access
Kazuhiko Minami
cond-mat.stat-mechmath-phmath.MP
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Kazuhiko Minami

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