diff --git a/Documentation/Doc.idx b/Documentation/Doc.idx index dfa401cd7..ed8fc8722 100644 --- a/Documentation/Doc.idx +++ b/Documentation/Doc.idx @@ -1,14 +1,14 @@ -\indexentry{\texttt{Checkerboard}}{25} +\indexentry{\texttt{Checkerboard}}{24} +\indexentry{\texttt{Symm}}{25} \indexentry{\texttt{Symm}}{26} -\indexentry{\texttt{Symm}}{27} -\indexentry{\texttt{Symm}}{27} -\indexentry{\texttt{Precision Green} }{30} -\indexentry{\texttt{Precision Phase}}{30} -\indexentry{\path{NWrap}}{30} -\indexentry{\texttt{Square} }{76} -\indexentry{\path{Bilayer_square}}{77} -\indexentry{\path{N_leg_ladder}}{77} -\indexentry{\path{Honeycomb}}{77} -\indexentry{\texttt{Bilayer\_honeycomb}}{77} -\indexentry{\texttt{Triangular}}{78} -\indexentry{\texttt{Kagome}}{78} +\indexentry{\texttt{Symm}}{26} +\indexentry{\texttt{Precision Green} }{29} +\indexentry{\texttt{Precision Phase}}{29} +\indexentry{\path{NWrap}}{29} +\indexentry{\texttt{Square} }{77} +\indexentry{\path{Bilayer_square}}{78} +\indexentry{\path{N_leg_ladder}}{78} +\indexentry{\path{Honeycomb}}{78} +\indexentry{\texttt{Bilayer\_honeycomb}}{78} +\indexentry{\texttt{Triangular}}{79} +\indexentry{\texttt{Kagome}}{79} diff --git a/Documentation/doc.pdf b/Documentation/doc.pdf index 795b84519..ad103d82f 100644 Binary files a/Documentation/doc.pdf and b/Documentation/doc.pdf differ diff --git a/Documentation/sampling.tex b/Documentation/sampling.tex index 8eafe4f1e..064e09d82 100644 --- a/Documentation/sampling.tex +++ b/Documentation/sampling.tex @@ -74,7 +74,7 @@ \subsection{An explicit example of error estimation}\label{sec:autocorr} In order to determine the autocorrelation time, we calculate the correlation function \begin{equation} \label{eqn:autocorrel} - S_{\hat{O}}(t_{\textrm{Auto}})=\sum_{i=1}^{N_{\textrm{Bin}}-t_{\textrm{Auto}}}\frac{\left(O_i-\left\langle \hat{O}\right\rangle \right)\left(O_{i+t_{\textrm{Auto}}}-\left\langle \hat{O}\right\rangle \right)}{\left(O_i-\left\langle \hat{O}\right\rangle \right)\left(O_{i}-\left\langle \hat{O}\right\rangle \right)}\, , + S_{\hat{O}}(t_{\textrm{Auto}})=\frac{\sum_{i=1}^{N_{\textrm{Bin}}-t_{\textrm{Auto}}}\left(O_i-\left\langle \hat{O}\right\rangle \right)\left(O_{i+t_{\textrm{Auto}}}-\left\langle \hat{O}\right\rangle \right)}{\sum_{i=1}^{N_{\textrm{Bin}}-t_{\textrm{Auto}}}\left(O_i-\left\langle \hat{O}\right\rangle \right)\left(O_{i}-\left\langle \hat{O}\right\rangle \right)}\, , \end{equation} where $O_i$ refers to the Monte Carlo estimate of the observable $\hat{O}$ in the $i^{\text{th}}$ bin. This function typically shows an exponential decay and the decay rate defines the autocorrelation time. %