Recent neutron scattering experiments  have
sharpened the picture of an algebraic spin liquid phase
in CsNiCrF6, originally proposed by Zinkin et al. .
Anderson famously predicted that systems such as this,
with equal numbers of two magnetic species populating
a pyrochlore lattice, should favour configurations with
two of each type of ion present on every tetrahedron
With this in mind, we have studied a simple model of a
system comprised of equal numbers of two species of
Heisenberg spins, A and B, distributed randomly across
a pyrochlore lattice, but subject to the ice-rules like
constraint that each tetrahedron has two A and two B
type spins. We have characterized the ground state
magnetic behaviour for all possible combinations of the
three exchange interactions governing the system. This
reveals a large region of exchange parameter space for
which the system is in a spin liquid like state consisting
of a soup of single species, non-interacting,
antiferromagnetic loops. This configuration is robust
even in the presence of four ferromagnetic bonds per
tetrahedron. We demonstrate that the highly
constrained form of quenched disorder imposed on the
ion placement removes the possibility of a spin glass
transition from this cooperative paramagnetic regime.
We go on to discuss how the underlying structural
configuration leads to algebraic magnetic correlations,
manifested in the familiar bow-tie structure factor. This
model is also susceptible to strong finite size influences.
A system with finite size will be unable to develop the
correct loop distribution to produce the bow-tie structure
factor. We are currently investigating how such effects
manifest themselves and the implications for more
controllable arrays such as can be achieved with, for
example, artificial spin ice.
 T. Fennel et al., unpublished.
 M. P. Zinkin et al., Phys. Rev. B 56, 11786 (1997)
 P. W. Anderson, Phys. Rev. 102, 1008 (1956)