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 two-dimensional crystal of paramagnetic colloidal particles is induced by a magnetic field $H$. At the transition field $H_{\text{s}}$, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length $\xi \propto |H^2-H_{\text{s}}^2{|}^{-1/2}$. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is $d_{\text{u}}=2$. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

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• Fractal fluctuations at mixed-order transitions in interdependent networks
• Unified framework for hybrid percolation transitions based on microscopic dynamics
• Mixed-order transition in the antiferromagnetic quantum Ising chain in a field
• Statistical analysis of phase formation in 2D colloidal systems
• Nonequilibrium phases and phase transitions of the XY-model
• Hysteresis and criticality in hybrid percolation transitions
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Pattern Description of Quantum Phase Transitions in the Transverse Antiferromagnetic Ising Model with a Longitudinal Field
• Exact results for the extreme Thouless effect in a model of network dynamics
• Quantum Potts chain in alternating field