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More is different.

Philip W. Anderson
- 04 Aug 1972 - 
- Vol. 177, Iss: 4047, pp 393-396
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This article is published in Science.The article was published on 1972-08-04. It has received 3150 citations till now. The article focuses on the topics: MEDLINE & Scientific enterprise.

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Book ChapterDOI

Reduction and Renormalization

TL;DR: In this paper, a discussion of J. Willard Gibbs' famous caution concerning the connections between thermodynamic properties and statistical mechanical properties is presented, in light of relatively recent work in statistical physics on the existence of the thermodynamic limit and the explanation of critical behavior using the renormalization group apparatus.
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Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials.

TL;DR: An intuitive and quantitatively accurate conceptual formalism is developed that maps the two-dimensional elastic problem into that of nonlinear interaction of elastic charges, which offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability, and aspects of the postinstability state.
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The Natural Science Underlying Big History

TL;DR: No new science is needed to describe cosmic evolution's major milestones at a deep and empirical level; Quantitative models and experimental tests imply that a remarkable simplicity underlies the emergence and growth of complexity for a wide spectrum of known and diverse systems.
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Aspects of symmetry, topology and anomalies in quantum matter

TL;DR: In this paper, the authors explore the properties of gapped many-body quantum systems including symmetry-protected topological states (SPTs) and topologically ordered states (TOs).
References
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Quasi-particles and gauge invariance in the theory of superconductivity

TL;DR: In this paper, it was shown that the Meissner effect can be maintained in the quasi-particle picture by taking into account a certain class of corrections to the chargecurrent operator due to the phonon and Coulomb interaction.
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Random-Phase Approximation in the Theory of Superconductivity

TL;DR: In this paper, a generalization of the random-phase approximation of the theory of Coulomb correlation energy is applied to the superconductivity theory, and it is shown that most elementary excitations have the Bardeen-Cooper-Schrieffer energy gap spectrum, but there are collective excitations also.
Journal ArticleDOI

An Approximate Quantum Theory of the Antiferromagnetic Ground State

TL;DR: In this paper, the ground state energy of the Kramers-Heller theory of ferromagnetic ground states has been investigated and its properties were shown to lie within limits found elsewhere on rigorous grounds.
Journal ArticleDOI

Coherent Excited States in the Theory of Superconductivity: Gauge Invariance and the Meissner Effect

TL;DR: In this article, it was shown that the non-gauge-invariant terms in the Hamiltonian of Bardeen, Cooper, and Schrieffer have an effect on these states which vanishes in the weak coupling limit.
Journal ArticleDOI

Wave propagation in the early stages of aggregation of cellular slime molds.

TL;DR: A detailed theory of the velocity of propagation of the acrasin pulse responsible for the aggregation of some of the cellular slime molds is presented and it is shown that there is a critical density of amebae below which the waves cannot propagate.