Mixed-order phase transition in a colloidal crystal

Abstract

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid–solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field H. At the transition field Hs, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length ξ ∝ |H2 − Hs2|−1/2. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is du = 2. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.