Ultrasoft Classical Systems at Zero Temperature.

At low temperatures, classical ultrasoft particle systems develop interesting phases via the self-assembly of particle clusters. In this study, we reach analytical expressions for the energy and the density interval of the coexistence regions for general ultrasoft pairwise potentials at zero temperatures. We use an expansion in the inverse of the number of particles per cluster for an accurate determination of the different quantities of interest. Differently from previous works, we study the ground state of such models, in two and three dimensions, considering an integer cluster occupancy number. The resulting expressions were successfully tested in the small and large density regimes for the Generalized Exponential Model α, varying the value of the exponent.

Cluster self-assembly condition for arbitrary interaction potentials.

We present a sufficient criterion for the emergence of cluster phases in an ensemble of interacting classical particles with repulsive two-body interactions. Through a zero-temperature analysis in the low density region we determine the relevant characteristics of the interaction potential that make the energy of a two-particle cluster-crystal become smaller than that of a simple triangular lattice in two dimensions. The method leads to a mathematical condition for the emergence of cluster crystals in terms of the sum of Fourier components of a regularized interaction potential, which can be in principle applied to any arbitrary shape of interactions. We apply the formalism to several examples of bounded and unbounded potentials with and without cluster-forming ability. In all cases, the emergence of self-assembled cluster crystals is well captured by the presented analytic criterion and verified with known results from molecular dynamics simulations at vanishingly temperatures. Our work generalises known results for bounded potentials to repulsive potentials of arbitrary shape.

Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid.

Monodisperse ensembles of particles that have cluster crystalline phases at low temperatures can model a number of physical systems, such as vortices in type-1.5 superconductors, colloidal suspensions, and cold atoms. In this work, we study a two-dimensional cluster-forming particle system interacting via an ultrasoft potential. We present a simple mean-field characterization of the cluster-crystal ground state, corroborating with Monte Carlo simulations for a wide range of densities. The efficiency of several Monte Carlo algorithms is compared, and the challenges of thermal equilibrium sampling are identified. We demonstrate that the liquid to cluster-crystal phase transition is of first order and occurs in a single step, and the liquid phase is a cluster liquid.

On the mechanism behind the inverse melting in systems with competing interactions.

The competition between a short range attractive interaction and a nonlocal repulsive interaction promote the appearance of modulated phases. In this work we present the microscopic mechanisms leading to the emergence of inverse transitions in such systems by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions. We identify the specific connections between the characteristic energy of the homogeneous and modulated phases and the observed reentrant behaviors in the phase diagram. In particular, we find that reentrance is appreciable when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other, and for systems in which the local order parameter is limited. In the asymptotic limit of high energy cost of the homogeneous phase we observe that the degree of reentrance decreases exponentially with the ratio of the characteristic energy cost of homogeneous and modulated phases. These mean-field results are confronted with Langevin simulations of an effective coarse grained model, confirming the expected extension of the reentrance in the phase diagram. These results shed new light on many systems undergoing inverse melting transitions by qualitatively improving the understanding of the interplay of entropy and energy around the inverse melting points.

Phase-change switching in 2D via soft interactions.

We present a new type of phase-change behavior relevant for information storage applications, that can be observed in 2D systems with cluster-forming ability. The temperature-based control of the ordering in 2D particle systems depends on the existence of a crystal-to-glass transition. We perform molecular dynamics simulations of models with soft interactions, demonstrating that the crystalline and amorphous structures can be easily tuned by heat pulses. The physical mechanism responsible for this behavior is a self-assembled polydispersity, that depends on the cluster-forming ability of the interactions. Therefore, the range of real materials that can perform such a transition is very wide in nature, ranging from colloidal suspensions to vortex matter. The state of the art in soft matter experimental setups, controlling interactions, polydispersity and dimensionality, makes it a very fertile ground for practical applications.

Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors.

At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster crystal. In the present Letter, we explore the out-of-equilibrium dynamics for a two-dimensional realization, which is relevant to superconducting materials with multiscale intervortex forces. We find that, for small temperatures following a quench, the suppression of the thermally activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in terms of an "effective polydispersity" induced by multiscale interactions. This demonstrates that a vortex glass can form in clean systems of thin films of "type-1.5" superconductors. An additional setup to study this physics can be layered superconducting systems, where the shape of the effective vortex-vortex interactions can be engineered.

Monodisperse cluster crystals: Classical and quantum dynamics.

We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium low-temperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquidlike long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: Zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics.