  Magnetism arising from coupled spin and spatial degrees of freedom underlies
the properties of a broad array of physical systems. We study here the
interplay between correlations in spin and space for the quantum compass model
in a finite external field, using quantum Monte Carlo methods. We find that
finite temperatures cant the spin and space (bond) correlations, with
increasing temperature even reorienting spin correlations between orthogonal
spatial directions. We develop a coupled mean field theory to understand this
effect in terms of the underlying quantum critical properties of crossed Ising
chains in transverse fields and an effective field that weakens upon increasing
temperature. Thermal canting offers an experimental signature of spin-bond
anisotropy.
