Editing 1-dimensional Ising model

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 <math> S_j </math> can be either -1 or +1.

The partition function of the system will be:

<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.

to be continued ...
@@ Line 1: / Line 1: @@
-The '''1-dimensional Ising model''' is an [[Ising Models| Ising model]] that consists of  a system with <math> N </math> spins in a row. The energy of the system is given by
+Model:
+Consider a system with <math> N </math> spins in a row.
-:<math>  U = -J \sum_{i=1}^{N-1} S_{i} S_{i+1} </math>,
+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 <math> S_j </math> can be either -1 or +1.
-The [[partition function]] of the system will be:
+The partition function of the system will be:
-:<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,
-and <math> K = J/k_B T </math>
-:<math> Q_{N} = \sum_{S_1} \sum_{S_2} e^{K S_1S_2} \sum_{S_3} e^{K S_2 S_3} \cdots \sum_{S_{N-1}} e^{K S_{N-2} S_{N-1}}\sum_{S_{N}} e^{K S_{N-1} S_{N} }
-</math>
-Performing the sum of the possible values of <math> S_{N} </math> we get:
-:<math> Q_{N} = \sum_{S_1} \sum_{S_2} e^{K S_1S_2} \sum_{S_3} e^{K S_2 S_3} \cdots \sum_{S_{N-1}} e^{K S_{N-2} S_{N-1}} \left[ 2 \cosh ( K S_{N-1} ) \right]
-</math>
-Taking into account that <math> \cosh(K) = \cosh(-K) </math>
-:<math> Q_{N} = \sum_{S_1} \sum_{S_2} e^{K S_1S_2} \sum_{S_3} e^{K S_2 S_3} \cdots \sum_{S_{N-1}} e^{K S_{N-2} S_{N-1}} \left[ 2 \cosh ( K ) \right]
-</math>
-Therefore:
-:<math> Q_{N} = \left( 2 \cosh K \right) Q_{N-1} </math>
-:<math> Q_N = 2^{N} \left( \cosh K \right)^{N-1} \approx ( 2 \cosh K )^N </math>
+<math> Q_N = \sum_{\Omega^N }  \exp \left[ - K \sum_{i=1}^{N-1} S_i S_{i+1}  \right]</math>,
-The [[Helmholtz energy function]] in the [[thermodynamic limit]] will be
+where <math> \Omega^N </math> represents the possible configuration of the N ''spins'' of the system.
-:<math> A = - N k_B T \log \left( 2 \cosh K \right) </math>
+to be continued ...
-==References==
-# Rodney J. Baxter  "Exactly Solved Models in Statistical Mechanics", Academic Press (1982)  ISBN 0120831821 Chapter 2 (freely available [http://tpsrv.anu.edu.au/Members/baxter/book/Exactly.pdf pdf])
-[[Category: Models]]