207 citations · 2.4k across the 59 of their papers we have counts for
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A geometric perspective on the scaling limits of critical Ising and models
Michael Aizenman
The lecture delivered at the \emph{Current Developments in Mathematics} conference (Harvard-MIT, 2021) focused on the recent proof of the Gaussian structure of the scaling limits o…
Dimerization and Néel order in different quantum spin chains through a shared loop representation
Michael Aizenman, Hugo Duminil-Copin, Simone Warzel
The ground states of the spin- antiferromagnetic chain with a projection-based interaction and the spin- XXZ-chain at anisotropy param…
Marginal triviality of the scaling limits of critical 4D Ising and models
Michael Aizenman, Hugo Duminil-Copin
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussi…
Exponential decay of correlations in the 2D random field Ising model
Michael Aizenman, Matan Harel, Ron Peled
An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement…
A power-law upper bound on the correlations in the 2D random field Ising model
Michael Aizenman, Ron Peled
As first asserted by Y. Imry and S-K Ma, the famed discontinuity of the magnetization as function of the magnetic field in the two dimensional Ising model is eliminated, for all te…
Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
Michael Aizenman, Hugo Duminil-Copin, Vincent Tassion +1
The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological consi…