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models:spin_models [2018/05/07 07:24]
jakobadmin [Overview]
models:spin_models [2020/04/12 14:47] (current)
jakobadmin
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 ====== Spin Models ====== ====== Spin Models ======
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 <tabbox Overview> ​ <tabbox Overview> ​
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 Spin models can be classified depending on how many different states are possible at each lattice site and if the set of possible states is continuous or discrete. Spin models can be classified depending on how many different states are possible at each lattice site and if the set of possible states is continuous or discrete.
  
-  * Models with a discrete set of states are called Potts models.  +  * Models with a discrete set of states are called ​**Potts models**.  
-  * Models with a continuous set of states are called n-Vector models+  * Models with a continuous set of states are called ​**n-Vector models**.
  
 Within these subcategories we have different models depending on how many states there are in total. For Potts models, the number of orientations that are possible is denoted by $Q$. For n-vector models, the dimension in which the continuous set of states live at each node is denoted by an $n$.  Within these subcategories we have different models depending on how many states there are in total. For Potts models, the number of orientations that are possible is denoted by $Q$. For n-vector models, the dimension in which the continuous set of states live at each node is denoted by an $n$. 
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-<​blockquote>​"​Empirically,​ one finds that all systems in nature belong to one of a comparatively small number of such universality classes. Two specific microscopic interaction Hamiltonians appear almost sufficient to encompass the universality classes necessary for static critical phenomena.  +<​blockquote>​
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-[...] [T]he Q-state Potts model (Potts, 1952; Wu, 1982) [and] the n-vector model (Stanley, 1968).+
  
 The first of these is the Q-state Potts model (Potts, 1952; Wu, 1982). One assumes that each spin i can be in one of Q possible discrete orientations $\chi_i$ $(\chi_i =,​1,​2,​\ldots,​Q)$. If two neighboring spins i and j are in the same orientation,​ then they contribute an amount $-J$ to the total energy of a configuration. If i and j are in different orientations,​ they contribute nothing. Thus the interaction Hamiltonian is  The first of these is the Q-state Potts model (Potts, 1952; Wu, 1982). One assumes that each spin i can be in one of Q possible discrete orientations $\chi_i$ $(\chi_i =,​1,​2,​\ldots,​Q)$. If two neighboring spins i and j are in the same orientation,​ then they contribute an amount $-J$ to the total energy of a configuration. If i and j are in different orientations,​ they contribute nothing. Thus the interaction Hamiltonian is 
models/spin_models.1525670662.txt.gz · Last modified: 2018/05/07 05:24 (external edit)