Related papers: Phase Coexistence for the Hard-Core Model on ${\ma…
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…
We formulate a continuous version of the well known discrete hardcore (or independent set) model on a locally finite graph, parameterized by the so-called activity parameter $\lambda > 0$. In this version, the state or "spin value" $x_u$ of…
For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice…
For different phases to coexist in equilibrium at constant temperature $T$ and pressure $P$, the condition of equal chemical potential $\mu$ must be satisfied. This condition dictates that, for a single-component system, the maximum number…
The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that…
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…
We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter $\lambda$, each matching $M$ is assigned a weight $\lambda^{|M|}$. The counting…
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…
Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist…
In this paper, we study the Hard Core (HC) model with a countable set $\mathbb Z$ of spin values on a Cayley tree of order $k=2$. This model is defined by a countable set of parameters (that is, the activity function $\lambda_i>0$, $i\in…
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…
We consider fertile three-state Hard-Core (HC) models with the activity parameter $\lambda>0$ on a Cayley tree. It is known that there exist four types of such models: wrench, wand, hinge, and pipe. These models arise as simple examples of…
In this paper, we focus on studying non-probability Gibbs measures for a Hard Core (HC) model on a Cayley tree of order $k\geq 2$, where the set of integers $\mathbb Z$ is the set of spin values. It is well-known that each Gibbs measure,…
In this paper we study Hard-Core model on a Cayley tree. For a normal divisor of index four new conditions for uniqueness and non-uniqueness of weakly periodic Gibbs measures are found.
It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…
We use an extension of fundamental measure theory to lattice hard-core fluids to study the phase diagram of two different systems. First, two-dimensional parallel hard squares with edge-length $\sigma=2$ in a simple square lattice. This…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
We study the computational complexity of approximately counting the number of independent sets of a graph with maximum degree Delta. More generally, for an input graph G=(V,E) and an activity lambda>0, we are interested in the quantity…
We consider a nearest-neighbor $p$-adic $\l$-model with spin values $\pm 1$ on a Cayley tree of order $k\geq 1$. We prove for the model there is no phase transition and as well as the unique $p$-adic Gibbs measure is bounded if and only if…
We consider the (scalar) gradient fields $\eta=(\eta_b)$--with $b$ denoting the nearest-neighbor edges in $\Z^2$--that are distributed according to the Gibbs measure proportional to $\texte^{-\beta H(\eta)}\nu(\textd\eta)$. Here…