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- The Ising model is a simple model of magnetism where two-valued spins live on the vertices of a graph and interact through the graph’s edges with energy based on their relative orientations12. The spins are usually arranged in a lattice, allowing each spin to interact with its neighbors2. The Ising model is a fundamental paradigm of discrete statistical mechanics3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.The Ising model is a simple model of magnetism, where two-valued spins σi = ±1 live on the vertices of a graph and interact through the graph’s edges with en-ergy −Jijσiσj.web.mit.edu/8.334/www/grades/projects/projects23…The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.en.wikipedia.org/wiki/Ising_modelIn this lecture we review the Ising model which provides a fundamental paradigm of discrete statistical mechanics. Some of the ideas introduced in this chapter will be encountered again later. 1 (Pairwise) Ising Model on a General Graph Let G = (V; E) be an undirected graph with set of vertices V and set of edges E.documents.epfl.ch/groups/i/ip/ipg/www/2010-2011/…
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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 the case of ferromagnetic interaction
• In the case of … 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 … 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 The Theoretical and Statistical Ising Model: A Practical Guide in …
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Geometric properties of the complete-graph Ising model in the …