Critical scaling of the mutual information in two-dimensional disordered Ising models

Sriluckshmy, P. V.; Mandal, Ipsita

doi:10.1088/1742-5468/aab1b6

Cited by 10 publications

(11 citation statements)

References 34 publications

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“…Mutual information is an entropy-based quantification of the "shared information" of two random variables quantifying how knowledge of one decreases the uncertainty of the other and vice versa 54 . Mutual information peaks at the critical temperature of spin systems during second-order transitions and has been widely used in detecting phase transitions 55,56 ; an advantage of this statistic is its ability to quantify non-linear dependence, unlike Moran's I and covariance which only account for linear dependence.…”

Section: Methodsmentioning

confidence: 99%

Spatial early warning signals of social and epidemiological tipping points in a coupled behaviour-disease network

Phillips

Anand

Bauch

2020

Sci Rep

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critical transition in dynamical systems 30,31. For instance, critical slowing down can precede both first-and second-order transitions 31,32 and is accompanied by the divergence of correlation length in a physical system 33. Many statistics have been used to study EWS in spatially extended systems; temporal 34,35 and spatial correlation 36,37 have been found to precede transitions in spreading processes. Other measurements have been applied to spin systems, where each site in a lattice may be in one of two possible states, possibly partially dependent on the state of neighbouring sites. The spin model has also been applied to opinion dynamics; a simple voter model with binary opinion dynamics is analogous to a physical spin system, where particles represent agents and spins represent different opinions 38. Consensus formation can be seen as a second-order phase transition to an ordered state (where all spins are aligned). In this regime, knowledge of the opinion of a single agent predicts the opinion of all other agents in the system 39. Since the transition in finite networks is smooth 40 , the distance across the network over which the opinions of connected agents are strongly correlated increases smoothly; this is analogous to divergence of the correlation length of a physical system 41. Above some critical temperature, disordered systems take the form of a spin glass. In a spatial opinion model, this describes a state where opinions between neighbours are generally uncorrelated 42. On a static network, this state induces a larger number of edges between dissimilar neighbours as compared to that of consensus regimes. This is related to join count statistics, where the numbers of edges between like neighbours are compared to the number between dislike neighbours as a test of geographical distribution. This is arguably the most natural and well-defined measure for graphs presenting binary data and is used for spatial analysis 43. The necessity of disease surveillance and early warning signals for outbreaks has been discussed in multiple contexts, from epidemic mitigation to bioterrorism prevention 44-46. Potential mitigation of unnecessary expense motivates us to find reliable EWS that remain easily computable on large high-resolution data sets. Furthermore, the study of EWS in coupled disease-behaviour multiplex networks has received relatively little attention, suggesting a significant gap in the literature. Our objective is to evaluate and compare the relative merits of the mutual information, Moran's I, Geary's C and join count statistics as EWS of the occurrence of epidemics and changes in aggregate opinion on a coupled disease-behaviour network model. We use three differently parametrised models (V1, V2 and V3) coupling a binary vaccination opinion dynamic to an SIRV epidemic process. The resulting trends in the EWS for model V2 will be explored in the Results and Discussion sections, with V1 and V3 presented in Supplementary Information S5. The outline of this paper is as follows: the Methods section wil...

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Section: Methodsmentioning

confidence: 99%

Spatial early warning signals of social and epidemiological tipping points in a coupled behaviour-disease network

Phillips

Anand

Bauch

2020

Sci Rep

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“…Much efforts focused on the behaviour of the mutual information. For instance, it has been suggested [25][26][27][28][29][30] that the mutual information exhibits a crossing for different sizes at a finite-temperature critical point, similar to more traditional tools in critical phenomena, such as the Binder cumulant [31].…”

Section: Introductionmentioning

confidence: 95%

Entanglement and classical fluctuations at finite-temperature critical points

Wald¹,

Arias²,

Alba³

2020

J. Stat. Mech.

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We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature T and of the quantum parameter g, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any g and T , the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of g, T , the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any g, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough T . The vanishing of the negativity defines a "death line", which we characterise analytically at small g. Importantly, for any finite T the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit T → 0. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

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“…The sensitivity of MI to nonlinear dependence is certainly appealing in studies on GT [19,20,55] as well as in other fields of physics, including topological transition in the XY model [28], phase transition in a 2D disordered Ising model [53] and evaluation of the configurational entropy of liquid metals [25]. On the other hand, unlike the Pearson correlation coefficient, the MI evaluation requires knowledge of the distributions of random variables.…”

Section: Draftmentioning

confidence: 99%

Mutual Information in Molecular and Macromolecular Systems

Tripodo,

Puosi,

Malvaldi

et al. 2021

Preprint

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The relaxation properties of viscous liquids close to their glass transition (GT) have been widely characterised by the statistical tool of time correlation functions. However, the strong influence of ubiquitous non-linearities calls for new, alternative tools of analysis. In this respect, information theory-based observables and, more specifically, mutual information (MI) are gaining increasing interest. Here, we report on novel, deeper insight provided by MI-based analysis of molecular dynamics simulations of molecular and macromolecular glass-formers on two distinct aspects of transport and relaxation close to GT, namely dynamical heterogeneity (DH) and secondary Johari-Goldstein (JG) relaxation processes. In a model molecular liquid with significant DH, MI reveals two populations of particles organised in clusters having either filamentous or compact globular structures that exhibit different mobility and relaxation properties. In a model polymer melt, MI provides clearer evidence of JG secondary relaxation and sharper insight into its DH. It is found that both DH and MI between the orientation and the displacement of the bonds reach (local) maxima at the time scales of the primary and JG secondary relaxation. This suggests that, in (macro)molecular systems, the mechanistic explanation of both DH and relaxation must involve rotation/translation coupling.

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Critical scaling of the mutual information in two-dimensional disordered Ising models

Cited by 10 publications

References 34 publications

Spatial early warning signals of social and epidemiological tipping points in a coupled behaviour-disease network

Spatial early warning signals of social and epidemiological tipping points in a coupled behaviour-disease network

Entanglement and classical fluctuations at finite-temperature critical points

Mutual Information in Molecular and Macromolecular Systems

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