Stress hyperuniformity and transient oscillatory-exponential correlation decay as signatures of strength vs fragility in glasses

2021 ◽  
Vol 155 (19) ◽  
pp. 194501
Author(s):  
Anaël Lemaître
Keyword(s):  
Correlation Decay

scholarly journals The Complexity of Approximating the Matching Polynomial in the Complex Plane

2021 ◽  
Vol 13 (2) ◽  
pp. 1-37
Author(s):  
Ivona Bezáková ◽  
Andreas Galanis ◽  
Leslie Ann Goldberg ◽  
Daniel Štefankovič
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Maximum Degree ◽  
Negative Real Axis ◽  
Positive Real ◽  
Bounded Degree ◽  
Matching Polynomial ◽  
Correlation Decay ◽  
Connective Constant ◽  
General Complex

We study the problem of approximating the value of the matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in the complex plane. When γ is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs. For general complex values of γ, Patel and Regts, building on methods developed by Barvinok, showed that the problem admits an FPTAS on graphs of maximum degree Δ as long as γ is not a negative real number less than or equal to −1/(4(Δ −1)). Our first main result completes the picture for the approximability of the matching polynomial on bounded degree graphs. We show that for all Δ ≥ 3 and all real γ less than −1/(4(Δ −1)), the problem of approximating the value of the matching polynomial on graphs of maximum degree Δ with edge parameter γ is #P-hard. We then explore whether the maximum degree parameter can be replaced by the connective constant. Sinclair et al. showed that for positive real γ, it is possible to approximate the value of the matching polynomial using a correlation decay algorithm on graphs with bounded connective constant (and potentially unbounded maximum degree). We first show that this result does not extend in general in the complex plane; in particular, the problem is #P-hard on graphs with bounded connective constant for a dense set of γ values on the negative real axis. Nevertheless, we show that the result does extend for any complex value γ that does not lie on the negative real axis. Our analysis accounts for complex values of γ using geodesic distances in the complex plane in the metric defined by an appropriate density function.

scholarly journals Contraction: A Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems

2021 ◽  
Vol 185 (2) ◽  
Author(s):  
Shuai Shao ◽  
Yuxin Sun
Keyword(s):  
Partition Function ◽  
Approximation Algorithms ◽  
External Field ◽  
Spin System ◽  
Spin Systems ◽  
Interaction Parameters ◽  
Entire Family ◽  
Bounded Degree ◽  
Correlation Decay ◽  
Complex Valued

AbstractWe study the connection between the correlation decay property (more precisely, strong spatial mixing) and the zero-freeness of the partition function of 2-spin systems on graphs of bounded degree. We show that for 2-spin systems on an entire family of graphs of a given bounded degree, the contraction property that ensures correlation decay exists for certain real parameters implies the zero-freeness of the partition function and the existence of correlation decay for some corresponding complex neighborhoods. Based on this connection, we are able to extend any real parameter of which the 2-spin system on graphs of bounded degree exhibits correlation decay to its complex neighborhood where the partition function is zero-free and correlation decay still exists. We give new zero-free regions in which the edge interaction parameters and the uniform external field are all complex-valued, and we show the existence of correlation decay for such complex regions. As a consequence, we obtain approximation algorithms for computing the partition function of 2-spin systems on graphs of bounded degree for these complex parameter settings.

On correlation decay in low-dimensional systems

2013 ◽  
Vol 104 (2) ◽  
pp. 20004 ◽  
Author(s):  
Julia Slipantschuk ◽  
Oscar F. Bandtlow ◽  
Wolfram Just
Keyword(s):  
Correlation Decay ◽  
Low Dimensional

scholarly journals Deterministic counting of graph colourings using sequences of subgraphs

2020 ◽  
Vol 29 (4) ◽  
pp. 555-586
Author(s):  
Charilaos Efthymiou
Keyword(s):  
Free Energy ◽  
Spatial Correlation ◽  
Random Graph ◽  
Polynomial Time ◽  
Gibbs Distribution ◽  
Correlation Decay ◽  
Point Correlation ◽  
Graph Colourings ◽  
Point To Point

AbstractIn this paper we propose a polynomial-time deterministic algorithm for approximately counting the k-colourings of the random graph G(n, d/n), for constant d>0. In particular, our algorithm computes in polynomial time a $(1\pm n^{-\Omega(1)})$ -approximation of the so-called ‘free energy’ of the k-colourings of G(n, d/n), for $k\geq (1+\varepsilon) d$ with probability $1-o(1)$ over the graph instances.Our algorithm uses spatial correlation decay to compute numerically estimates of marginals of the Gibbs distribution. Spatial correlation decay has been used in different counting schemes for deterministic counting. So far algorithms have exploited a certain kind of set-to-point correlation decay, e.g. the so-called Gibbs uniqueness. Here we deviate from this setting and exploit a point-to-point correlation decay. The spatial mixing requirement is that for a pair of vertices the correlation between their corresponding configurations becomes weaker with their distance.Furthermore, our approach generalizes in that it allows us to compute the Gibbs marginals for small sets of nearby vertices. Also, we establish a connection between the fluctuations of the number of colourings of G(n, d/n) and the fluctuations of the number of short cycles and edges in the graph.

Correlation decay in low‐dimensional spin glasses

1994 ◽  
Vol 76 (10) ◽  
pp. 6186-6188 ◽  
Author(s):  
A. N. Kocharian ◽  
A. S. Sogomonian
Keyword(s):  
Spin Glasses ◽  
Correlation Decay ◽  
Low Dimensional

scholarly journals Time Reversibility, Correlation Decay and the Steady State Fluctuation Relation for Dissipation

Entropy ◽  
2013 ◽  
Vol 15 (12) ◽  
pp. 1503-1515 ◽  
Author(s):  
Debra Searles ◽  
Barbara Johnston ◽  
Denis Evans ◽  
Lamberto Rondoni
Keyword(s):  
Steady State ◽  
Time Reversibility ◽  
Correlation Decay ◽  
Fluctuation Relation

Correlation decay for an intermittent area-preserving map

1998 ◽  
Vol 246 (5) ◽  
pp. 407-411 ◽  
Author(s):  
Roberto Artuso ◽  
Andrea Prampolini
Keyword(s):  
Correlation Decay ◽  
Area Preserving

scholarly journals Correlation Decay in Random Decision Networks

2014 ◽  
Vol 39 (2) ◽  
pp. 229-261 ◽  
Author(s):  
David Gamarnik ◽  
David A. Goldberg ◽  
Theophane Weber
Keyword(s):  
Decision Networks ◽  
Correlation Decay
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