Related papers: High-density hard-core model on triangular and hex…
We study the Gibbs statistics of high-density hard-core configurations on a unit square lattice $\mathbb{Z}^2$, for a general Euclidean exclusion distance $D$. As a by-product, we solve the disk-packing problem on $\mathbb{Z}^2$ for disks…
We study dense packings of disks and related Gibbs distributions representing high-density phases in the hard-core model on unit triangular, honeycomb and square lattices. The model is characterized by a Euclidean exclusion distance $D>0$…
We study the hard-core model of statistical mechanics on a unit cubic lattice $\mathbb{Z}^3$, which is intrinsically related to the sphere-packing problem for spheres with centers in $\mathbb{Z}^3$. The model is defined by the sphere…
We confirm the list from \cite{MSS} of values $D$ for which the high-density hard-core model on $\mathbb{Z}^2$ with exceptional distance $D$ has infinitely many extremal Gibbs states. As a byproduct, we prove that for all $D>0$ there exists…
Recoverable systems provide coarse models of data storage on the two-dimensional square lattice, where each site reconstructs its value from neighboring sites according to a specified local rule. To study the typical behavior of recoverable…
The hard-core model has attracted much attention across several disciplines, representing lattice gases in statistical physics and independent sets in discrete mathematics and computer science. On finite graphs, we are given a parameter…
The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using…
In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high…
The extended Hubbard model with a nearest-neighbor Coulomb repulsion on the square lattice is studied to obtain insight into the phase diagram of cuprate high $T_c$ superconductors (HTS). To pursue the hidden-order scenario proposed in [S.…
We consider the hard-core model in $\mathbb{R}^2$, in which a random set of non-intersecting unit disks is sampled with an intensity parameter $\lambda$. Given $\varepsilon>0$ we consider the graph in which two disks are adjacent if they…
We perform a rigorous study of the identical sphere packing problem in $\mathbb{Z}^3$ and of phase transitions in the corresponding hard-core model. The sphere diameter $D>0$ and the fugacity $u\gg 1$ are the varying parameters of the…
The $k$-NN hard core lattice gas model on a square lattice, in which the first $k$ next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two…
Hard core lattice gas models are minimal models to study entropy driven phase transitions. In the $k$-NN lattice gas, a particle excludes all sites upto the $k$-th next-nearest neighbors from being occupied by another particle. As $k$…
In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice ${\mathbb Z}^2$ from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice ${\mathbb…
We consider random lattice triangulations of $n\times k$ rectangular regions with weight $\lambda^{|\sigma|}$ where $\lambda>0$ is a parameter and $|\sigma|$ denotes the total edge length of the triangulation. When $\lambda\in(0,1)$ and $k$…
We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with…
We study the hard-core model defined on independent sets, where each independent set I in a graph G is weighted proportionally to $\lambda^{|I|}$, for a positive real parameter $\lambda$. For large $\lambda$, computing the partition…
Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from…
We use Ginzburg-Landau theory to study the $H_{c2}$ transition in layered superconductors with field parallel to the layers, finding a continuous 3d freezing transition to a triangular vortex super-solid in the three-dimensional XY…
We study an intrinsic curvature model defined on fixed-connectivity triangulated lattices enclosing a spherical core by using the canonical Monte Carlo simulation technique. We find that the model undergoes a discontinuous transition of…