Editing Ising model
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The '''Ising model''' <ref>[http://dx.doi.org/10.1007/BF02980577 Ernst Ising "Beitrag zur Theorie des Ferromagnetismus", Zeitschrift für Physik A Hadrons and Nuclei '''31''' pp. 253-258 (1925)]</ref> | The '''Ising model''' is also known as the '''Lenz-Ising''' model <ref>[http://dx.doi.org/10.1007/BF02980577 Ernst Ising "Beitrag zur Theorie des Ferromagnetismus", Zeitschrift für Physik A Hadrons and Nuclei '''31''' pp. 253-258 (1925)]</ref>. For a history of the Lenz-Ising model see <ref>[http://dx.doi.org/10.1103/RevModPhys.39.883 S. G. Brush "History of the Lenz-Ising Model", Reviews of Modern Physics '''39''' pp. 883-893 (1967)]</ref> | ||
<ref>[http://dx.doi.org/10.1007/s00407-004-0088-3 Martin Niss "History of the Lenz-Ising Model 1920-1950: From Ferromagnetic to Cooperative Phenomena", Archive for History of Exact Sciences '''59''' pp. 267-318 (2005)]</ref> | |||
<ref>[http://dx.doi.org/10.1007/s00407-008-0039-5 Martin Niss "History of the Lenz–Ising Model 1950–1965: from irrelevance to relevance", Archive for History of Exact Sciences '''63''' pp. 243-287 (2009)]</ref>. | |||
The Ising model is commonly defined over an ordered lattice. | |||
Each site of the lattice can adopt two states, <math>S \in \{-1, +1 \}</math>. Note that sometimes these states are referred to as ''spins'' and the values are referred to as ''down'' and ''up'' respectively. | Each site of the lattice can adopt two states, <math>S \in \{-1, +1 \}</math>. Note that sometimes these states are referred to as ''spins'' and the values are referred to as ''down'' and ''up'' respectively. | ||
The energy of the system is the sum of pair interactions | The energy of the system is the sum of pair interactions | ||
between nearest neighbors. | between nearest neighbors. | ||
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where <math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math> \langle ij \rangle </math> indicates that the sum is performed over nearest neighbors, and | where <math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math> \langle ij \rangle </math> indicates that the sum is performed over nearest neighbors, and | ||
<math> S_i </math> indicates the state of the i-th site, and <math> K </math> is the coupling constant | <math> S_i </math> indicates the state of the i-th site, and <math> K </math> is the coupling constant. | ||
==1-dimensional Ising model== | ==1-dimensional Ising model== | ||
:''Main article: [[1-dimensional Ising model]]'' | :''Main article: [[1-dimensional Ising model]]'' |