The Worm Process for the Ising Model is Rapidly Mixing
Reads0
Chats0
TLDR
In this article, the worm process for the zero-field ferromagnetic Ising model was shown to be fast and robust on all finite connected graphs, and at all temperatures, and a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.Abstract:
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.read more
Citations
More filters
Posted Content
Random cluster dynamics for the Ising model is rapidly mixing
Heng Guo,Mark Jerrum +1 more
TL;DR: It is shown that the mixing time of Glauber (single edge update) dynamics for the random cluster model at $q=2$ is bounded by a polynomial in the size of the underlying graph.
Proceedings ArticleDOI
Random cluster dynamics for the ising model is rapidly mixing
Heng Guo,Mark Jerrum +1 more
TL;DR: It is shown that the mixing time of Glauber (single edge update) dynamics for the random cluster model at $q=2$ is bounded by a polynomial in the size of the underlying graph.
Journal ArticleDOI
Lifted worm algorithm for the Ising model.
TL;DR: The results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids.
Posted Content
Lee-Yang zeros and the complexity of the ferromagnetic Ising model on bounded-degree graphs
TL;DR: P-hardness for approximating the partition function on graphs of maximum degree $\Delta$ when $b$, the edge-interaction parameter, is in the interval $(0,\frac{\Delta-2}{\Delta}]$ and $\lambda$ is a non-real on the unit circle.
Posted Content
Lower bounds for testing graphical models: colorings and antiferromagnetic Ising models
TL;DR: In this article, it was shown that identity testing is hard in the same regime of parameters where structure learning is known to require a super-polynomial number of samples, and that there is no polynomial running time identity testing algorithm unless RP=NP.
References
More filters
Book
Graph Theory
TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
Book
Approximation Algorithms
TL;DR: Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field.
Book
Markov Chains and Mixing Times
TL;DR: Markov Chains and Mixing Times as mentioned in this paper is an introduction to the modern approach to the theory of Markov chains and its application in the field of probability theory and linear algebra, where the main goal is to determine the rate of convergence of a Markov chain to the stationary distribution.
Journal ArticleDOI
Nonuniversal critical dynamics in Monte Carlo simulations
TL;DR: A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality, despite the fact that the algorithm violates dynamic universality at second-order phase transitions.
Journal ArticleDOI
On the random-cluster model: I. Introduction and relation to other models
C.M. Fortuin,P.W. Kasteleyn +1 more
TL;DR: It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.