We propose and solve a simple model describing secondary structure formatio
n in random hetero-polymers. It describes monomers with a combination of on
e-dimensional short-range interactions (representing steric forces and hydr
ogen bonds) and infinite-range interactions (representing polarity forces).
We solve our model using a combination of mean-field and random-field tech
niques, leading to phase diagrams exhibiting second-order transitions betwe
en folded, partially folded and unfolded states, including regions where fo
lding depends on initial conditions. Our theoretical results, which are in
excellent agreement with numerical simulations, lead to an appealing physic
al picture of the folding process: the polarity forces drive the transition
to a collapsed state, the steric forces introduce monomer specificity and
the hydrogen bonds stabilize the conformation by damping the frustration-in
duced multiplicity of states.