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jy:results [2018/07/30 06:37] – [7.30.18 Inverse Problem data] yilingjy:results [2019/09/16 09:22] (current) – [2019-09-16 :Case N1: long tail antiferromagentic] yiling
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 +[[namespace:page#here|2019-09-16 :Case N1: long tail antiferromagentic]]
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 ====== 2018-07-2 :The solutions to the inverse Ising problem  ====== ====== 2018-07-2 :The solutions to the inverse Ising problem  ======
  
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 ====== 7.19.18 Inverse Problem  ====== ====== 7.19.18 Inverse Problem  ======
  
-The mean field theory (nMF): +{{page>dynstat:mean-field}}
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-$\mathbf{J}^\text{nMF}=-\mathbf{C}^{-1}, (i \neq j) $, +
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-$h_{i}^\text{nMF}=\tanh^{-1}\left< s_{i} \right>-\sum_{j=1}^{N} J{ij}^\text{nMF}\left< s_{j} \right> $ . +
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-The independent-pair theory (IP): +
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-$J_{ij}^\text{pair}=0.25*\ln\left[ \frac{(1+m_{i}+m_{j}+C_{ij}^{*}) (1-m_{i}-m_{j}+C_{ij}^{*})} {(1-m_{i}+m_{j}-C_{ij}^{*})(1+m_{i}-m_{j}-C_{ij}^{*})} \right]$, with $C_{ij}^{*}=C_{ij}+m_{i}m_{j} , (i \neq j)$ +
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-$h_{i}^\text{pair}=0.5*\ln\left( \frac{1+m_{i}} {1-m_{i}} \right)-\sum_{j=1}^{N} J_{ij}^\text{pair} m_{j}$. +
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-The Thouless-Anderson-Palmer theory (TAP): +
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-$\mathbf{C}^{-1}+J_{ij}^\text{TAP}+2(J_{ij}^\text{TAP})^{2}m_{i}m_{j}=0 , (i \neq j)$ +
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-$h_{i}^\text{TAP}=h_{i}^\text{nMF}-m_{i}\sum_{i=1}^{N} (J_{ij}^\text{TAP})^{2} (1-m_{j})^{2}$. +
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-The Sessak and Monasson theory (SM): +
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-$J_{ij}^\text{SM}=J_{ij}^\text{nMF}+J_{ij}^\text{pair}-\frac{C_{ij}}{(1-m_{i}^{2})(1-m_{j}^{2})-C_{ij}^{2}} , (i \neq j)$ +
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-$h_{i}^\text{SM}=0.5*\ln\left( \frac{1+m_{i}} {1-m_{i}} \right)-\sum_{j=1}^{N} J_{ij}^\text{SM} m_{j}$.+
  
 The coefficient of $R^{2}$ is: The coefficient of $R^{2}$ is: