Frustration and topology in the phase behavior of solute-frustrated $q$-clock models

Abstract

Frustration can enhance fluctuations and create new and interesting phase behavior. When combined with the ability to host topological defects, frustration can increase the complexity of a system's phase diagram through topological and frustrated topological transitions. To understand the interplay of frustration and topology on phase behavior, we introduce and study solute-frustrated $q$-clock (SF$q$C) models, in which solute sites are added to the $q$-clock model, a lattice model where each spin can take one of $q$ orientations. The $q$-clock model can exhibit spontaneous symmetry breaking and topological transitions, and the interaction between the spins and a solute frustrates the system, in essence by creating a fixed lower bound on the concentration of positive topological defects or vortices. We perform Monte Carlo simulations and develop theoretical descriptions of SF$q$C models with $q=4$ and $q=6$ to understand their phase behavior. We find that these systems exhibit rich phase diagrams that depend on the choice of parameters. In particular, SF$q$C models have a wide range of interesting low-temperature phases, including the presence of strongly frustrated domains and the absence of long-range order. We also find topological effects even at low temperatures; for instance, we find that topological defects can drive crystallization. We anticipate these results to guide the development of materials that take advantage of frustration and topology to tune phase behavior and fluctuations.