The two-dimensional Jordan-Wigner transformation is used to investigate the
zero temperature spin-Peierls transition for an anisotropic two-dimensional XY
model in adiabatic limit. The phase diagram between the dimerized (D) state and
uniform (U) state is shown in the parameter space of dimensionless interchain
coupling h(=J⊥/J) and spin-lattice coupling η. It is found
that the spin-lattice coupling η must exceed some critical value ηc
in order to reach the D phase for any finite h. The dependence of ηc on
h is given by −1/lnh for h→0 and the transition between U and D
phase is of first-order for at least h>10−3.Comment: 2 eps figures, considerable revisions were mad