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 17:14, 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
in other words
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.