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100 Years of the (Critical) Ising Model on the Hypercubic Lattice

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arxiv 2208.00864 v1 pith:LET5QWKR submitted 2022-08-01 math.PR math-phmath.MP

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keywords modelcriticalhypercubicisinglatticeyearsamazingarticle
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We take the occasion of this article to review one hundred years of the physical and mathematical study of the Ising model. The model, introduced by Lenz in 1920, has been at the cornerstone of many major revolutions in statistical mechanics. We wish, through its history, to outline some of these amazing developments. We restrict our attention to the ferromagnetic nearest-neighbour model on the hypercubic lattice, and essentially focus on what happens at or near the so-called critical point.

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Cited by 2 Pith papers

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  1. A switching identity for cable-graph loop soups and Gaussian free fields

    math.PR 2025-02 accept novelty 8.0 of 10

    Conditioning two cable-graph points to lie in the same Brownian loop-soup cluster adds an odd-numbered Poisson cloud of Brownian excursions between them, yielding an exact law for the conditional cluster and its GFF analogue.

  2. Classical and quantum spin liquids

    cond-mat.str-el 2025-01 unverdicted

    Classical and quantum spin liquids are zero-temperature disordered magnetic phases that can be classified by their correlations, excitations, and emergent gauge structure.

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