A Magnetic Model of the Tetragonal-Orthorhombic Transition in the Cuprates

It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings ({\it e.g.} on a body-centered tetragonal lattice) generically exhibits two thermal phase transitions with lowering temperature -- an upper transition at $T_{TO}$ (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower N\'{e}el transition at $T_{N}$ at which spin-rotation symmetry is broken. Although this is the same sequence of transitions observed in La$_2$CuO$_4$, in the Heisenberg model (without additional lattice degrees of freedom) $(T_{TO}-T_N) /T_N$ is much smaller than is observed. The model may apply to the bilayer cuprate La$_2$CaCuO$_6$, in which the transitions are nearly coincident.