Conformal Invariance in Mechanical Models

The problem of a single bead on a rotating hoop has been studied extensively in the past, and serves as a mechanical model for the Landau theory of phase transitions. We consider a situation with infinitely many beads on a rotating hoop, with each bead coupled to its nearest neighbours with springs. The system approximately obeys the Landau-Ginzburg Hamiltonian, and shows features characteristic of ferromagnetism, such as domain formation and long-range correlations at criticality. This is confirmed using numerical simulations. Moreover, solitons hosted by the system map directly to instanton solutions in the single-bead-on-a-hoop problem.