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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.
• 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-neighbor coupling in the zero magnetic … 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 … 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. Consider an Ising model with 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 See more
Wikipedia text under CC-BY-SA license WEBWhat about higher dimensions? A nifty argument due to R. Peierls shows that there will be a finite temperature phase transition for the Ising model on the square lattice 1. Consider the Ising model, in zero magnetic …
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 …
WEBSep 20, 2022 · 4.5: Ising model - Exact and numerical results. In order to evaluate the main prediction ( 4.4.14) of the Weiss theory, let us now discuss the exact (analytical) and quasi-exact (numerical) results …
The Ising model and counting graphs - University of …
WEBThe Ising model is perhaps the most famous and widely studied model in statistical mechanics. It models the effect of temperature and external magnetic fields on the properties of a magnet. When a piece of iron is …
Optimal structure and parameter learning of Ising models
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Max-cut equivalence with most likely assignment to an Ising model
Geometric properties of the complete-graph Ising model in the …
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