Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph
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We study complexity and approximation of MIN WEIGHTED NODE COLORING in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove ...
We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a nonplanar way at T=0. This model, consisting of coupled trihedra (or Ising-RP3 model), encompasses Ising (chiral) de ...
Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s,k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite graph ...
The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...
In this paper we evaluate the free energy of the dilute p-spin model at finite temperature. Franz et al gave the first step to rigourize the replica solution for the dilute p-spin model by proving that the solution given by the Parisi replica scheme is a l ...
Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite grap ...
We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...
We discuss the situation where attractive and repulsive portions of the interparticle potential both contribute significantly to glass formation. We introduce the square-well potential as prototypical model for this situation, and reject the Baxter model a ...