Related papers: Long range order in a hard disk model in statistic…
We perform a rigorous study of the Gibbs statistics of high-density hard-core random configurations on a unit triangular lattice $\mathbb{A}_2$ and a unit honeycomb graph $\mathbb{H}_2$, for any value of the (Euclidean) repulsion diameter…
Time crystals are many-body systems whose ground state spontaneously breaks time-translation symmetry and thus exhibits long-range spatiotemporal order and robust periodic motion. Using hydrodynamics, we have recently shown how an…
Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution,…
We study nuclear relaxation in the presence of localized electrons in a two-dimensional electron gas in a disordered delta-doped semiconductor heterostructure and show that this method can reliably probe their magnetic interactions and…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The emergence of long-range order at low temperatures in atomistic systems with continuous symmetry is a fundamental, yet poorly understood phenomenon in Physics. To address this challenge we study a discrete microscopic model for an…
Within the framework of the algebra of canonical commutation relations in Euclidean space, a long range order between particles in bounded regions is established in states with a sufficiently large particle number. It occurs whenever…
Vibrated polar disks have been used experimentally to investigate collective motion of driven particles, where fully-ordered asymptotic regimes could not be reached. Here we present a model reproducing quantitatively the single, binary and…
We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance $r$ with probability $P(r) \propto r^{-\al}$. The…
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites).…
A granular-matter model is exactly solved, where disks of two sizes and weights in alternating sequence are confined to a narrow channel. The axis of the channel is horizontal and its plane vertical. Disk sizes and channel width are such…
The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration…
An accurate description of a columnar liquid crystal of hard disks at high packing fractions is presented using an improved free-volume theory. It is shown that the orientational entropy of the disks in the one-dimensional fluid direction…
We investigate a modified version of the $AB$ random sequential adsorption model. Specifically, this model involves the deposition of two distinct types of particles onto a lattice, with the constraint that different types cannot occupy…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
This paper proposes a phase space to compare the static packings of a granular system compatible to a macrostate that is set by the external stress. The nature of this phase space is analyzed, showing that the consideration of the allowed…