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

Effective potential approach to hybrid synchronization transitions

“…1. This criterion was confirmed by theoretical and experimental studies of the crystallization of colloidal magnets, in which the free energy is zero throughout the region m = [0, m * ] [17]. We note that the Landau theory criterion for the HPT was established in equilibrium thermal systems.…”

“…The terms mixed-order and HPT may often be used interchangeably. Examples appear in various equilibrium and nonequilibrium systems, including the Ising model with long-range interactions in one dimension [2][3][4][5], the Ashkin-Teller (AT) model on scale-free networks [6], kcore percolation [7][8][9][10], DNA denaturation [11][12][13], jamming [14][15][16], crystallization of colloidal magnets [17], and synchronization [18][19][20].…”

Competing contagion processes: Complex contagion triggered by simple contagion

“…[22][23][24][25] A hybrid transition is also predicted in a model of spin chains with long-range interactions, 55 DNA denaturation, 56 and jamming, 57,58 and recently observed experimentally in a colloidal crystal. 59 An example of how to identify a phase transition is shown in terms of the graphical solution of f (R) with z = 10 and n = 4 in the limit ρ → 0 [ Fig. 2(c)].…”

Statistical analysis of phase formation in 2D colloidal systems

“…Of particular interest are studies of frustration [6], network formation [7][8][9][10][11][12], crystallization [13][14][15][16][17] or the glass transition [18][19][20]. The beauty of microscopy in this context is that the structures are imaged in real space and can be directly visualized.…”