1-dimensional Ising model: Difference between revisions
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m (New page: Model: Consider a system with <math> N </math> spins in a row. The energy of the system will be given by <math> U = -K \sum_{i=1}^{N-1} S_{i} S_{i+1} </math>, where each variable <mat...) |
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The energy of the system will be given by | The energy of the system will be given by | ||
<math> U = - | <math> U = -J \sum_{i=1}^{N-1} S_{i} S_{i+1} </math>, | ||
where each variable <math> S_j </math> can be either -1 or +1. | where each variable <math> S_j </math> can be either -1 or +1. | ||
| Line 10: | Line 10: | ||
The partition function of the system will be: | The partition function of the system will be: | ||
<math> Q_N = \sum_{\Omega^N } \exp \left[ | <math> Q_N = \sum_{\Omega^N } \exp \left[ K \sum_{i=1}^{N-1} S_i S_{i+1} \right]</math>, | ||
where <math> \Omega^N </math> represents the possible configuration of the N ''spins'' of the system | |||
where <math> \Omega^N </math> represents the possible configuration of the N ''spins'' of the system, | |||
and <math> K = J/k_B T </math> | |||
to be continued ... | to be continued ... | ||
Revision as of 11:22, 23 February 2007
Model: Consider a system with spins in a row.
The energy of the system will be given by
,
where each variable can be either -1 or +1.
The partition function of the system will be:
,
![{\displaystyle Q_{N}=\sum _{\Omega ^{N}}\exp \left[K\sum _{i=1}^{N-1}S_{i}S_{i+1}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1419d045395f90f5727c9e80f5550a0aa103109)
where represents the possible configuration of the N spins of the system,
and
to be continued ...