A paper by a group led by Prof. Joshua Socolar to Physical Review E has been highlighted as an Editor's Suggestion. Entitled "Emergence of limit-periodic order in tiling models," the paper describes the theory of formation of an ordered solid that is not a periodic crystal. Read it here. The lead author on the paper was graduate student Catherine Marcoux, and in addition to Socolar the team included Prof. Patrick Charbonneau and two Duke physics majors, Travis Byington and Zongjin Qian, who wrote honors theses on portions of this work.
One visualization of the limit-periodic phase consists of a lattice of cubic "particles," each with an internal decoration that breaks the cubic symmetry. The particles are all identical, but the pattern of their orientations is nonperiodic. The accompanying figure shows how the decorations join to form helices with different radii, and the theory indicates that at zero temperature there will be helices with radii larger than any specified size. The paper included analytical results, numerical calculations of free energies, and Monte Carlo simulations of the sequence of phase transitions that guides the system to the limit-periodic state. At each successive transition, lattices of larger radius helices form. Remarkably, a slow quench selects the limit-periodic phase even if the true ground state is a periodic crystal. Marcoux and Socolar are now working with colleagues in the Triangle MRSEC to create a physical realization of a closely related phase in a colloidal monolayer.
Department of Physics
