Critical Phenomena in 3.99 Dimensions

Wilson, Kenneth G.; Wolfe, Hugh C.; Graham, C. D.; Rhyne, J. J.

doi:10.1063/1.2947035

Cited by 4 publications

(3 citation statements)

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“…K. G. Wilson gave the talk ‘Critical Phenomena in 3.99 Dimensions’ where he explained in more detail how renormalization theory could overcome the breakdown of Landau theory. Apart from inducing a flood of calculations of critical exponents in various systems, Wilson’s theory not only “gave new life to the theory of critical phenomena” [ 45 ] but led also advance in other fields like high-energy physics or physics of turbulence. This wide-reaching aspect is reflected in the citation rate (see Figure 4 a) and recently in Paul Fendley’s judgment: “The RG is not only the way to understand critical phenomena quantitatively, but lies at the very core of why theoretical physics is so effective” [ 46 ].…”

Section: Sharing Science In the Time Of The Cold Warmentioning

confidence: 99%

Knotting the MECO Network

Folk

2021

Entropy

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The Conferences of the Middle European Cooperation in Statistical Physics (MECO) were created as an attempt to establish and maintain an exchange between scientists in the fields of statistical and condensed matter physics from Western and Eastern countries, overcoming the hurdles of the Iron Curtain. Based on personal remembrance and historical resources, the genesis and further development of MECO meetings is described. The annual meetings were interrupted in 1991 by the Yugoslav War but were re-established in 1993 and continue today. Although the fall of the Iron Curtain and the European Research programs changed the situation for the meetings considerably, the ties created by MECO still are useful to help scientific exchange. The history of European (and not only) statistical physics and the history of the MECO are tightly intertwined. It started in a time where an essential breakthrough has been achieved in statistical physics describing the features near phase transitions. In addition to the merging of solid-state physics and field theory concepts, the application of numerical methods (Monte Carlo methods) added a new pillar besides exact solutions and experiments to check theoretical models. In the following, the scientific emphasis (in general) has changed from the traditional fields of the first MECO to complexity and interdisciplinary themes as well.

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Section: Sharing Science In the Time Of The Cold Warmentioning

confidence: 99%

Knotting the MECO Network

Folk

2021

Entropy

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“…However, situations where we introduce some degree of dilution (e.g. Erdös-Rényi graph), yet preserving the homogeneity of the structure and an extensive coordination number, can be looked and treated as mean field models.2 In that context the long-range interactions are unacceptable because the involved couplings are of electromagnetic nature, hence displaying power-law decay with the distance.3 It is worth mentioning that the Wilson-Kadanoff renormalization equations [37,38,39] turn out to be exact in models with power law interactions as those built on the hierarchical lattice that we are going to consider. 2 k+1 i<j brings a contribution scaling like 2 2(k+1) ∼ N 2 , while the pre-factor scales as 2 −2σ(k+1) ∼ N −2σ , thus, when σ < 1 2 the intensive energy is overall divergent in the thermodynamic limit k → ∞.…”

mentioning

confidence: 99%

“…3 It is worth mentioning that the Wilson-Kadanoff renormalization equations [37,38,39] turn out to be exact in models with power law interactions as those built on the hierarchical lattice that we are going to consider. 2 k+1 i<j brings a contribution scaling like 2 2(k+1) ∼ N 2 , while the pre-factor scales as 2 −2σ(k+1) ∼ N −2σ , thus, when σ < 1 2 the intensive energy is overall divergent in the thermodynamic limit k → ∞.…”

mentioning

confidence: 99%

Hierarchical neural networks perform both serial and parallel processing

et al. 2015

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In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal-to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns grows at most logarithmical with the system size, we prove that these non-mean-field Hopfield-like networks display a richer phase diagram than their classical counterparts. In particular, these networks are able to perform serial processing (i.e. retrieve one pattern at a time through a complete rearrangement of the whole ensemble of neurons) as well as parallel processing (i.e. retrieve several patterns simultaneously, delegating the management of different patterns to diverse communities that build network). The tune between the two regimes is given by the rate of the coupling decay and by the level of noise affecting the system. The price to pay for those remarkable capabilities lies in a network's capacity smaller than the mean field counterpart, thus yielding a new budget principle: the wider the multitasking capabilities, the lower the network load and vice versa. This may have important implications in our understanding of biological complexity.

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Renormalization-group and mode-coupling theories of critical dynamics

Kawasaki

Gunton

1976

Phys. Rev. B

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Critical Phenomena in 3.99 Dimensions

Cited by 4 publications

References 0 publications

Knotting the MECO Network

Knotting the MECO Network

Hierarchical neural networks perform both serial and parallel processing

Renormalization-group and mode-coupling theories of critical dynamics

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