Order Out of Disorder in a Gas of Elastic Quantum Strings in2+1Dimensions

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 always solidifies, by a mechanism which is the quantum analog of the entropic interactions known from soft condensed matter physics.