  We present a statistical field theory to describe large length scale effects
induced by solutes in a cold and otherwise placid liquid. The theory divides
space into a cubic grid of cells. The side length of each cell is of the order
of the bulk correlation length of the bulk liquid. Large length scale states of
the cells are specified with an Ising variable. Finer length scale effects are
described with a Gaussian field, with mean and variance affected by both the
large length scale field and by the constraints imposed by solutes. In the
absence of solutes and corresponding constraints, integration over the Gaussian
field yields an effective lattice gas Hamiltonian for the large length scale
field. In the presence of solutes, the integration adds additional terms to
this Hamiltonian. We identify these terms analytically. They can provoke large
length scale effects, such as the formation of interfaces and depletion layers.
We apply our theory to compute the reversible work to form a bubble in liquid
water, as a function of the bubble radius. Comparison with molecular simulation
results for the same function indicates that the theory is reasonably accurate.
Importantly, simulating the large length scale field involves binary arithmetic
only. It thus provides a computationally convenient scheme to incorporate
explicit solvent dynamics and structure in simulation studies of large
molecular assemblies.
