Spiky phases of smooth membranes. Implications for smooth strings

We point out a possible mechanism by which smooth surfaces can become spiky as the constant of curvature stiffness falls below a certain critical value. This happens either in a single first-order transition, or in a sequence of two Kosterlitz-Thouless-like transitions. There may also be additional phases in which the spikes form a hexagonal solid-like array or a disordered liquid-like structure. Our discussion suggests that there exist smooth strings between quarks.