Equivalence between the two-dimensional Ising model and the quantum XY chain with randomness and with open boundary
Graduate School of Mathematics, Nagoya University - Nagoya, 464-8602, Japan
Received: 17 September 2014
Accepted: 8 October 2014
The equivalence between the two-dimensional Ising model and the one-dimensional quantum XY model is generalized to the cases with alternating/random interactions and with periodic/free boundary conditions. It is proved that the eigenstate for the maximum eigenvalue of the transfer matrix of the two-dimensional Ising model corresponds to the ground state of the Hamiltonian of the one-dimensional XY model, which certifies direct relations between the physical quantities of the two models.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 75.10.Hk – Classical spin models / 75.10.Pq – Spin chain models
© EPLA, 2014