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- Vertex_model abstract "A vertex model is a type of statistical mechanics model in which the Boltzmann weights are associated with a vertex in the model (representing an atom or particle). This contrasts with a nearest-neighbour model, such as the Ising model, in which the energy, and thus the Boltzmann weight of a statistical microstate is attributed to the bonds connecting two neighbouring particles. The energy associated with a vertex in the lattice of particles is thus dependent on the state of the bonds which connect it to adjacent vertices. It turns out that every solution of the Yang-Baxter equation with spectral parameters in a tensor product of vector spaces yields an exactly-solvable vertex model.Although the model can be applied to various geometries in any number of dimensions, with any number of possible states for a given bond, the most fundamental examples occur for two dimensional lattices, the simplest being a square lattice where each bond has two possible states. In this model, every particle is connected to four other particles, and each of the four bonds adjacent to the particle has two possible states, indicated by the direction of an arrow on the bond. In this model, each vertex can adopt possible configurations. The energy for a given vertex can be given by , with a state of the lattice is an assignment of a state of each bond, with the total energy of the state being the sum of the vertex energies. As the energy is often divergent for an infinite lattice, the model is studied for a finite lattice as the lattice approaches infinite size. Periodic or domain wall boundary conditions may be imposed on the model.".
- Vertex_model thumbnail Lattice2.jpg?width=300.
- Vertex_model wikiPageExternalLink 1103909051.
- Vertex_model wikiPageID "4924962".
- Vertex_model wikiPageRevisionID "604497493".
- Vertex_model hasPhotoCollection Vertex_model.
- Vertex_model subject Category:Lattice_models.
- Vertex_model subject Category:Statistical_mechanics.
- Vertex_model type Assistant109815790.
- Vertex_model type CausalAgent100007347.
- Vertex_model type LatticeModels.
- Vertex_model type LivingThing100004258.
- Vertex_model type Model110324560.
- Vertex_model type Object100002684.
- Vertex_model type Organism100004475.
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- Vertex_model type YagoLegalActor.
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- Vertex_model comment "A vertex model is a type of statistical mechanics model in which the Boltzmann weights are associated with a vertex in the model (representing an atom or particle). This contrasts with a nearest-neighbour model, such as the Ising model, in which the energy, and thus the Boltzmann weight of a statistical microstate is attributed to the bonds connecting two neighbouring particles.".
- Vertex_model label "Vertex model".
- Vertex_model sameAs m.0cvgs8.
- Vertex_model sameAs Q7922777.
- Vertex_model sameAs Q7922777.
- Vertex_model sameAs Vertex_model.
- Vertex_model wasDerivedFrom Vertex_model?oldid=604497493.
- Vertex_model depiction Lattice2.jpg.
- Vertex_model isPrimaryTopicOf Vertex_model.
