|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{DISPLAYTITLE:''n''-vector model}}
| | She is known by the title of Myrtle Shryock. Years in the past we moved to Puerto Rico and my family loves it. I am a meter reader but I plan on altering it. To play baseball is the hobby he will never quit doing.<br><br>Feel free to visit my web blog :: [http://lync.io/dietmealdelivery74619 meal delivery service] |
| The ''' ''n''-vector model''' or '''O(''n'') model''' is one of the many highly simplified models in the branch of physics known as [[statistical mechanics]]. In the ''n''-vector model, ''n''-component, unit length, classical [[spin (physics)|spins]] <math> \mathbf{s}_i </math> are placed on the vertices of a [[lattice (group)|lattice]]. The [[Hamiltonian mechanics|Hamiltonian]] of the n-vector model is given by:
| |
| | |
| :<math>H = -J{\sum}_{<i,j>}\mathbf{s}_i \cdot \mathbf{s}_j</math>
| |
| | |
| where the sum runs over all pairs of neighboring spins <math><i,j></math> and <math>\cdot</math> denotes the standard Euclidean inner product. Special cases of the n-vector model are:
| |
| | |
| :<math>n=0</math> || The [[Self-avoiding walk|Self-Avoiding Walks (SAW)]]
| |
| :<math>n=1</math> || The [[Ising model]] | |
| :<math>n=2</math> || The [[XY model]] | |
| :<math>n=3</math> || The [[Heisenberg model (classical)|Heisenberg model]] | |
| :<math>n=4</math> || [[Toy model]] for the [[Higgs sector]] of the [[Standard Model]]
| |
| | |
| The general mathematical formalism used to describe and solve the ''n''-vector model and certain generalizations are developed in the article on the [[Potts model]].
| |
| | |
| ==References==
| |
| * P.G. de Gennes, Phys. Lett. A, 38, 339 (1972) noticed that the <math>n=0</math> case corresponds to the SAW.
| |
| * George Gaspari, Joseph Rudnick, Phys. Rev. B, 33, 3295 (1986) discuss the model in the limit of <math>n</math> going to 0.
| |
| | |
| [[Category:Lattice models]]
| |
| {{physics-stub}}
| |
She is known by the title of Myrtle Shryock. Years in the past we moved to Puerto Rico and my family loves it. I am a meter reader but I plan on altering it. To play baseball is the hobby he will never quit doing.
Feel free to visit my web blog :: meal delivery service