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models:spin_models

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models:spin_models [2018/05/07 07:24]
jakobadmin [Overview]
models:spin_models [2018/05/07 07:24]
jakobadmin [Overview]
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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.txt · Last modified: 2020/04/12 14:47 by jakobadmin