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Ising model - Wikipedia
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or … See more
The thermodynamic limit exists as long as the interaction decay is $${\displaystyle J_{ij}\sim |i-j|^{-\alpha }}$$ with α > 1.
• In … See moreIn three as in two dimensions, the most studied case of the Ising model is the translation-invariant model on a cubic lattice with nearest … See more
The most studied case of the Ising model is the translation-invariant ferromagnetic zero-field model on a d-dimensional lattice, namely, Λ = Z , Jij = 1, h = 0.
No phase transition in one dimension
In his 1924 PhD thesis, Ising solved the model for the d = 1 … See moreOne of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials … See more
Definitions
The Ising model can often be difficult to evaluate numerically if there are many states in the system. … See more• In the ferromagnetic case there is a phase transition. At low temperature, the Peierls argument proves positive magnetization for the nearest neighbor case and then, by the Griffiths inequality, also when longer range interactions are added. Meanwhile, … See more
Wikipedia text under CC-BY-SA license The Ising Model - Stanford University
The Theoretical and Statistical Ising Model: A …
WEBOct 8, 2021 · The “Ising model” refers to both the statistical and the theoretical use of the same equation. In this article, we introduce both uses and contrast their differences. We accompany the conceptual …
Frontiers | Ising formulations of many NP problems
Computational complexity continuum within Ising formulation of …
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ISING MODEL - ETH Z
The Ising model and counting graphs - University of British …
4.5: Ising model - Exact and numerical results - Physics LibreTexts
Optimal structure and parameter learning of Ising models
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