Global Flip Research Articles

Finitary codings for gradient models and a new graphical representation for the six‐vertex model

AbstractIt is known that the Ising model on at a given temperature is a finitary factor of an i.i.d. process if and only if the temperature is at least the critical temperature. Below the critical temperature, the plus and minus states of the Ising model are distinct and differ from one another by a global flip of the spins. We show that it is only this global information which poses an obstruction to being finitary by showing that the gradient of the Ising model is a finitary factor of i.i.d. at all temperatures. As a consequence, we deduce a volume‐order large deviation estimate for the energy. Results in the same spirit are shown for the Potts model, the so‐called beach model, and the six‐vertex model. We also introduce a coupling between the six‐vertex model with and a new Edwards–Sokal type graphical representation of it, which we believe is of independent interest.

Global Flip & Other Studies Workgroup Report

In their report, delegates of the Who Decides? workgroup of the OSI2016 conference put forth three proposals in which key stakeholders might convene to enact an economically viable and sustainable transformation of the current scholarly communications system to one of open access. The “Global Flip” workgroup of OSI2017 discussed the previous year’s “Proposal 3: Transformation: a “global flip” of research journals to open access” in which “libraries, publishers, and funders, convened by an organization with global standing, come together to redirect subscription funding toward transforming existing journals to open access publication.” Tasked with creating broad action plans for further research into the feasibility and impact of such a transformation, we identify a number of driving forces in the envisioned transformation, which could be further developed to assure its ultimate success as well as possible barriers to its desired fruition and suggested actions to remove them.

On the number of ground states of the Edwards–Anderson spin glass model

Les états fondamentaux du modèle de verre de spins de Edwards–Anderson (EA) sont étudiés sur des graphes infinis de degré fini. Les états fondamentaux sont les configurations de spins qui minimisent de manière locale l’Hamiltonien pour chaque ensemble fini de sommets. Un problème avec des implications importantes en physique et en mathématique est de déterminer le nombre d’états fondamentaux pour le modèle sur $\mathbb{Z}^{d}$ pour un $d>1$ donné. Ce problème est la version équivalente pour les modèles de verre de spins du problème du nombre de géodésiques infinies en percolation de premier passage et du nombre d’états fondamentaux du modèle d’Ising ferromagnétique désordonné. Il a été montré récemment par Newman, Stein et les deux auteurs que sur le demi-plan $\mathbb{Z}\times\mathbb{N}$, il existe un unique état fondamental (modulo un flip global des spins) produit par la limite faible des états fondamentaux des volumes finis pour un choix spécifique des conditions frontières. Dans cet article, nous étudions l’ensemble de tous les états fondamentaux sur le graphe infini $\mathbb{Z}\times\mathbb{N}$. Nous montrons que le nombre d’états fondamentaux est deux (correspondant à un flip global des spins) ou infini. Ceci est le premier résultat sur l’ensemble de tous les états fondamentaux pour une dimension non-triviale. Dans la première partie, nous développons des outils qui sont pertinents à la résolution du problème analogue sur $\mathbb{Z}^{d}$.

Decoding Binary Node Labels from Censored Edge Measurements: Phase Transition and Efficient Recovery

We consider the problem of clustering a graph G into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables Y = B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> x ⊕ Z, where B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> is the incidence matrix of a graph G, x is the vector of unknown vertex variables (with a uniform prior), and Z is a noise vector with Bernoulli (ε) i.i.d. entries. All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems. In particular, it corresponds to a stochastic block model or a correlation clustering problem with two communities and censored edges. Without noise, exact recovery (up to global flip) of x is possible if and only the graph G is connected, with a sharp threshold at the edge probability log (n)/n for Erdos-Renyi random graphs. The first goal of this paper is to determine how the edge probabilityp needs to scale to allow exact recovery in the presence of noise. Defining the degree rate of the graph by α = np/log(n), it is shown that exact recovery is possible if and only if α > 2/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + o(1/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). In other words, 2/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is the information theoretic threshold for exact recovery at low-SNR. In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate. For a deterministic graph G, defining the degree rate as α = d/log(n), where d is the minimum degree of the graph, it is shown that the proposed method achieves the rate α > 4((1 + λ)/(1 - λ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + o(1/(1 - 2ε) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), where 1-λ is the spectral gap of the graph G.

Connectivity-based localization of large-scale sensor networks with complex shape

We study the problem of localizing a large sensor network having a complex shape, possibly with holes. A major challenge with respect to such networks is to figure out the correct network layout, that is, avoid global flips where a part of the network folds on top of another. Our algorithm first selects landmarks on network boundaries with sufficient density, then constructs the landmark Voronoi diagram and its dual combinatorial Delaunay complex on these landmarks. The key insight is that the combinatorial Delaunay complex is provably globally rigid and has a unique realization in the plane. Thus an embedding of the landmarks by simply gluing the Delaunay triangles properly recovers the faithful network layout. With the landmarks nicely localized, the rest of the nodes can easily localize themselves by trilateration to nearby landmark nodes. This leads to a practical and accurate localization algorithm for large networks using only network connectivity. Simulations on various network topologies show surprisingly good results. In comparison, previous connectivity-based localization algorithms such as multidimensional scaling and rubberband representation generate globally flipped or distorted localization results.

CRITICAL DYNAMICS OF TWO-REPLICA CLUSTER ALGORITHMS

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent.

Quantum Monte Carlo Study on Magnetization Processes

A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of inefficiency of the update of the total magnetization. The method is demonstrated in the one dimensional antiferromagnetic Heisenberg model and the trimer model. We attempted various other Monte Carlo algorithms to study systems in the external field and compared their efficiency.

Ground-State and Thermodynamic Properties of the Quantum Mixed Spin-1/2-1/2-1-1 Chain

We investigate both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian $H=\sum_{\ell=1}^{N/4} (J_1\vecs_{4\ell-3}\cdot \vecs_{4\ell-2}+J_2\vecs_{4\ell-2}\cdot\vecS_{4\ell-1}+J_3\vecS_{4\ell-1}\cdot \vecS_{4\ell}+J_2\vecS_{4\ell}\cdot\vecs_{4\ell+1})$, where two $S=1/2$ spins ($\vecs_{4\ell-3}$ and $\vecs_{4\ell-2}$) and two S=1 spins ($\vecS_{4\ell-1}$ and $\vecS_{4\ell}$) are arranged alternatively. Inseveral limiting cases of $J_1$, $J_2$, and $J_3$ we apply the Wigner-Eckart theorem and carry out a perturbation calculation to examine the behavior of the massless lines where the energy gap vanishes. Performing a quantum Monte Carlo calculation without global flips at a sufficiently low temperature for the case where $J_1=J_3=1.0$ and $J_2>0$, we find that the ground state of the present system in this case undergoes a second-order phase transition accompanying the vanishing of the energy gap at $J_2=J_{2c$ with $J_{2 c} = 0.77 \pm 0.01$. We also find that the ground states for both $J_2 < J_{2 c$ and $J_2 > J_{2c$ can be understood by means of the valence-bond-solid picture. A quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account is carried out to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, it is found that the susceptibility per unit cell for $J_2=0.77$ with $J_1=J_3=1.0$ takes a finite value at absolute zero temperature and that the specific heat per unit cell versus temperature curve for $J_2=5.0$ with $J_1=J_3=1.0$ has a double peak.

Quantum Monte Carlo simulation of diluted Heisenberg antiferromagnets (S=1/2) on the square lattice

The effects of inhomogeneity in a system with strong quantum fluctuations are investigated by a quantum Monte Carlo simulation (QMC). The properties of an antiferromagnetic Heisenberg model with S=1/2 on the square lattice diluted by nonmagnetic impurities are investigated. The spatial distribution of the spin correlations near impurities are found to be largely enhanced. On the other hand, from the size dependence of the square of the staggered magnetization per spin, the correlations between largely separated spins are found to be smaller than in the nondiluted case. It has been found that the existence of nonmagnetic sites causes the ergodicity problem in QMC. In order to avoid this difficulty the authors introduce a new type of global flip. With this type of flip QMC gives good agreement with results obtained by exact diagonalization methods even for systems with highly concentrated impurities. The methodological points are also discussed in detail.