Related papers: Inapproximability After Uniqueness Phase Transitio…
A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…
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 study the complexity of approximating the partition function $Z_{\mathrm{Ising}}(G; \beta)$ of the Ising model in terms of the relation between the edge interaction $\beta$ and a parameter $\Delta$ which is an upper bound on the maximum…
One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This…
The hardcore model is a model of lattice gas systems which has received much attention in statistical physics, probability theory and theoretical computer science. It is the probability distribution over independent sets $I$ of a graph…
Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS…
We consider the problem of approximating the partition function of the hard-core model on planar graphs of degree at most 4. We show that when the activity lambda is sufficiently large, there is no fully polynomial randomised approximation…
We give a complete characterization of the two-state anti-ferromagnetic spin systems which are of strong spatial mixing on general graphs. We show that a two-state anti-ferromagnetic spin system is of strong spatial mixing on all graphs of…
The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in $\mathbb{R}^d$ with the formal Hamiltonian $H(\omega)=\text{Volume}(\cup_{x\in\omega} B_1(x))$, where $\omega$ is a locally finite configuration of points…
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…
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…
Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase…
Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core…
Taking (2+1)-dimensional pure Einstein gravity for arbitrary genus $g$ as a model, we investigate the relation between the partition function formally defined on the entire phase space and the one written in terms of the reduced phase…
We study Gibbs partition models, also known as composition schemes. Our main results comprehensively describe their phase diagram, including a phase transition from the convergent case described in Stufler (2018, Random Structures \&…
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…
Two-state spin systems is a classical topic in statistical physics. We consider the problem of computing the partition function of the systems on a bounded degree graph. Based on the self-avoiding tree, we prove the systems exhibits strong…
In this paper we consider a model with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k \geq 2$. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional…
We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…