https://networks.tir.tw/wiki/ 2026-04-28T20:43:16+00:00 https://networks.tir.tw/wiki/ https://networks.tir.tw/wiki/_media/logo.png text/html 2019-09-23T07:31:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://networks.tir.tw/wiki/jy:inverse?rev=1569223908&do=diff 7.19.18 Inverse Problem The mean field theory (nMF): $\mathbf{J}^\text{nMF}=-\mathbf{C}^{-1}, (i \neq j) $, $h_{i}^\text{nMF}=\tanh^{-1}\left< s_{i} \right>-\sum_{j=1}^{N} J{ij}^\text{nMF}\left< s_{j} \right> $ . The independent-pair theory (IP): $J_{ij}^\text{pair}=0.25*\ln\left[ \frac{(1+m_{i}+m_{j}+C_{ij}^{*}) (1-m_{i}-m_{j}+C_{ij}^{*})} {(1-m_{i}+m_{j}-C_{ij}^{*})(1+m_{i}-m_{j}-C_{ij}^{*})} \right]$, with $C_{ij}^{*}=C_{ij}+m_{i}m_{j} , (i \neq j)$ $h_{i}^\text{pair}=0.5*\ln\left( \fra… text/html 2019-09-16T09:22:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://networks.tir.tw/wiki/jy:results?rev=1568625753&do=diff 2019-09-16 :Case N1: long tail antiferromagentic 2018-07-2 :The solutions to the inverse Ising problem Method: Boltzmann learning Finding the external fields $h_{i}$ and the coupling parameters $J_{ij}$ can fit the same means and pairwise covariance as the experiment data, using the equations $\left<s_{i}\right>_{Ising} = \left<s_{i}\right>_{data} $ $\left<s_{i}s_{j}\right>_{Ising} = \left<s_{i}s_{j}\right>_{data} $. We can solve the equations by iterations $h_{i}=h_{i}+\delta h_{i}$$J_{i…