  We study inverse statistical mechanics: how can one design a potential
function so as to produce a specified ground state? In this paper, we show that
unexpectedly simple potential functions suffice for certain symmetrical
configurations, and we apply techniques from coding and information theory to
provide mathematical proof that the ground state has been achieved. These
potential functions are required to be decreasing and convex, which rules out
the use of potential wells. Furthermore, we give an algorithm for constructing
a potential function with a desired ground state.
