Dynamical scaling as a signature of multiple phase competition in Yb$_2$Ti$_2$O$_7$

$\rm Yb_2Ti_2O_7$ is a celebrated example of a pyrochlore magnet with highly-frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of $\rm Yb_2Ti_2O_7$. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple--phase competition, and confirm that a scaling collapse is also seen in semi--classical simulations of a microscopic model of $\rm Yb_2Ti_2O_7$. These results suggest a general picture for dynamics in systems with competing ground states.