Order-out-of-disorder in a gas of elastic quantum strings in 2+1 dimensions

A limiting case of a dynamical stripe state which is of potential significance to cuprate superconductors is considered: a gas of elastic quantum strings in 2+1 dimensions, interacting merely via a hard-core condition. It is demonstrated that this gas solidifies always, by a mechanism which is the quantum analogue of the entropic interactions known from soft condensed matter physics.