other glaring discrepancies remain. In this paper, we resolve these outstanding differences between theory and experiment by correcting the standard model of [[Cs$_2$CuCl$_4$]{}]{}.

It is important to emphasize that the corrections to Eq. (\[eq:Hexpt\]) [*must*]{} be small, because the standard model does an excellent job in explaining a large volume of experimental data. The parameters in Eq. (\[eq:Hexpt\]) were determined by high field measurements of single-magnon spectra,[@Coldea2002PRL] which leave little room for doubt of their correctness with relatively small error bars. Moreover, the same model, used at zero and intermediate fields, is quite successful in reproducing the full inelastic neutron spectrum, containing both continuum and magnon/triplon (sharp) contributions.[@kohno07:_spinon_and_tripl_in_spatial; @PhysRevLett.103.197203] Nevertheless, in some field orientations, entirely different low temperature phases are observed in experiment than are predicted by the standard model. Thus, we must somehow explain major [*qualitative*]{} differences in the ground states of [[Cs$_2$CuCl$_4$]{}]{} in a field by very small corrections to $H$, of no more than a few percent!

A key message of this paper is that, indeed, the frustration and quasi-one-dimensionality of this problem can and do amplify tiny terms in the Hamiltonian to the point where they actually control the ground state. Sensitivity to small perturbations is 