Driven surface diffusion with detailed balance and elastic phase transitions

Driven surface diffusion occurs, for example, in molecular beam epitaxy when particles are deposited under an oblique angle. Elastic phase transitions happen when normal modes in crystals become soft due to the vanishing of certain elastic constants. We show that these seemingly entirely disparate systems fall under appropriate conditions into the same universality class. We derive the field theoretic Hamiltonian for this universality class, and we use renormalized field theory to calculate critical exponents and logarithmic corrections for several experimentally relevant quantities.