Related papers: Approximability of the Six-vertex Model
We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…
This article surveys some of the work done in recent years on random simplicial complexes. We mostly consider higher-dimensional analogs of the well known phase transition in $G(n, p)$ theory that occurs at $p = \frac 1n$ . Our main…
Pairwise Compatibility Graphs (PCGs) form a tree-metric graph class that originated in phylogeny and has since attracted sustained interest in graph theory. Several natural generalizations have been proposed in order to overcome the…
We study the problem of complexity estimation in the context of parallelizing an advanced Branch and Bound-type algorithm over graphical models. The algorithm's pruning power makes load balancing, one crucial element of every distributed…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of…
Given a graph G, we investigate the question of determining the parity of the number of homomorphisms from G to some other fixed graph H. We conjecture that this problem exhibits a complexity dichotomy, such that all parity graph…
We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the analytical properties of the free energy of the model as the…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
A simple and robust spring-block model obeying threshold dynamics is introduced to study surface fracture of an overlayer subject to stress induced by adhesion to a substrate. We find a novel phase transition in the crack morphology and…
We study information theoretic quantities in models with three and four spin interactions. These models show distinctive characteristics compared to their nearest neighbour counterparts. Here, we quantify these in terms of the Nielsen…
Although it is well-known that some exponential family random graph model (ERGM) families exhibit phase transitions (in which small parameter changes lead to qualitative changes in graph structure), the behavior of other models is still…
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…
We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
Monte Carlo simulation has been performed on a classical two dimensional XY- model with a modified form of interaction potential to investigate the role of topological defects on the phase transition exhibited by the model. In simulations…
Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we…
Starting from a finite simple graph $G$, for each eigenvalue $\theta$ of its adjacency matrix one can construct a convex polytope $P_G(\theta)$, the so called $\theta$-eigenpolytop of $G$. For some polytopes this technique can be used to…
We discuss the correspondence between models solved by Bethe ansatz and classical integrable systems of Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric 6-vertex model parametrized by…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…