XY model: Difference between revisions
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The '''XY model''', also known as the ''O(2)'' model, is a Heisenberg ferromagnetic with an easy-plane anisotropy. | The '''XY model''', also known as the ''O(2)'' model because of its symmetry group, is a Heisenberg ferromagnetic with an easy-plane anisotropy. The [[Hamiltonian]] is given by | ||
:<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math> | |||
in other words | |||
:<math>H=-J{\sum}_{\langle i,j\rangle}\cos(\theta_i-\theta_j)</math> | |||
where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant. | |||
==Random field XY model (RFXY)== | ==Random field XY model (RFXY)== | ||
==XY universality class== | ==XY universality class== | ||
Revision as of 16:14, 22 January 2008
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The XY model, also known as the O(2) model because of its symmetry group, is a Heisenberg ferromagnetic with an easy-plane anisotropy. The Hamiltonian is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}}
in other words
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H=-J{\sum}_{\langle i,j\rangle}\cos(\theta_i-\theta_j)}
where the sum runs over all pairs of nearest neighbour spins, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{S}} , and where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J} is the coupling constant.