  We identify the low energy effective Hamiltonian that is expected to describe
the low temperature properties of the frustrated magnet
$\mathrm{Ca}_{10}\mathrm{Cr}_{7}\mathrm{O}_{28}$. Motivated by the fact that
this effective Hamiltonian has $S=3/2$ effective moments as its degrees of
freedom, we use semiclassical spinwave theory to study the $T=0$ physics of
this effective model and argue that singular spinwave fluctuations destabilize
the spiral order favoured by the exchange couplings of this effective
Hamiltonian. We also use a combination of classical Monte-Carlo simulations and
molecular dynamics, as well as analytical approximations, to study the physics
at low, nonzero temperatures. The results of these nonzero temperature
calculations capture the liquid-like structure factors observed in the
temperature range accessed by recent experiments. Additionally, at still lower
temperatures, they predict that a transition to nematic order in the bond
energies reflects itself in the spin channel in the form of a crossover to a
regime with large but finite correlation length for spiral spin correlations
and a corresponding slowing down of spin dynamics.

Strongly Correlated Electrons