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I am trying to typeset Pfaffian for the 2D Ising model. The structure of the Pffafian is given below

enter image description here

The code is

\[\mathrm{Pf} =
\begin{pmatrix}
  a_{12} & a_{13} & a_{14} & a_{15} & a_{16} & a_{17} & a_{18} & a_{19} & a_{1,10} & a_{1,11} & a_{1,12} & a_{1,13} & a_{1,14} & a_{1,15} & a_{1,16} \\
& a_{23} & a_{24} & a_{25} & a_{26} & a_{27} & a_{28} & a_{29} & a_{2,10} & a_{2,11} & a_{2,12} & a_{2,13} & a_{2,14} & a_{2,15} & a_{2,16} \\
&  & a_{34} & a_{35} & a_{36} & a_{37} & a_{38} & a_{39} & a_{3,10} & a_{3,11} & a_{3,12} & a_{3,13} & a_{3,14} & a_{3,15} & a_{3,16} \\
&  &  & a_{45} & a_{46} & a_{47} & a_{48} & a_{49} & a_{4,10} & a_{4,11} & a_{4,12} & a_{4,13} & a_{4,14} & a_{4,15} & a_{4,16} \\
&  &  &  & a_{56} & a_{57} & a_{58} & a_{59} & a_{5,10} & a_{5,11} & a_{5,12} & a_{5,13} & a_{5,14} & a_{5,15} & a_{5,16} \\
&  &  &  &  & a_{67} & a_{68} & a_{69} & a_{6,10} & a_{6,11} & a_{6,12} & a_{6,13} & a_{6,14} & a_{6,15} & a_{6,16} \\
 &  &  &  &  &  & a_{78} & a_{79} & a_{7,10} & a_{7,11} & a_{7,12} & a_{7,13} & a_{7,14} & a_{7,15} & a_{7,16} \\
 &  &  &  &  &  &  & a_{89} & a_{8,10} & a_{8,11} & a_{8,12} & a_{8,13} & a_{8,14} & a_{8,15} & a_{8,16} \\
&  &  &  &  &  &  &  & a_{9,10} & a_{9,11} & a_{9,12} & a_{9,13} & a_{9,14} & a_{9,15} & a_{9,16} \\
&  &  &  &  &  &  &  &  & a_{10,11} & a_{10,12} & a_{10,13} & a_{10,14} & a_{10,15} & a_{10,16} \\
&  &  &  &  &  &  &  &  &  & a_{11,12} & a_{11,13} & a_{11,14} & a_{11,15} & a_{11,16} \\
&  &  &  &  &  &  &  &  &  &  & a_{12,13} & a_{12,14} & a_{12,15} & a_{12,16} \\
&  &  &  &  &  &  &  &  &  &  &  & a_{13,14} & a_{13,15} & a_{13,16} \\
&  &  &  &  &  &  &  &  &  &  &  &  & a_{14,15} & a_{14,16} \\
&  &  &  &  &  &  &  &  &  &  &  &  &  & a_{15,16} \\
\end{pmatrix}
\]

As shown in the figure above, I could not adjust the left bracket. Can someone please help to resolve this?

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    please always post a full test document so people can run it to see the issue. You have shown an image of a lot of subscripted D and shown a fragment of code that won't run but if completed would make a lot of subscripted a, how are they related? But don't use pmatrix use matrix then you will not get the () and you can add suitable | at the start of the first row and after the matrix. Commented Jun 22 at 8:53

1 Answer 1

3

I'd use an empty delimiter on the left, setting \mathrm{PF}=( in the first cell.

I reduced the separation, but with the standard text width there's still an overfull. Adjust for your document.

\documentclass{article}
\usepackage{amsmath}

\setcounter{MaxMatrixCols}{20}

\begin{document}

\[
\left.
\setlength{\arraycolsep}{2pt}
\begin{matrix}
\mathrm{Pf} =
  ( a_{12} & a_{13} & a_{14} & a_{15} & a_{16} & a_{17} & a_{18} & a_{19} & a_{1,10} & a_{1,11} & a_{1,12} & a_{1,13} & a_{1,14} & a_{1,15} & a_{1,16} \\
& a_{23} & a_{24} & a_{25} & a_{26} & a_{27} & a_{28} & a_{29} & a_{2,10} & a_{2,11} & a_{2,12} & a_{2,13} & a_{2,14} & a_{2,15} & a_{2,16} \\
&  & a_{34} & a_{35} & a_{36} & a_{37} & a_{38} & a_{39} & a_{3,10} & a_{3,11} & a_{3,12} & a_{3,13} & a_{3,14} & a_{3,15} & a_{3,16} \\
&  &  & a_{45} & a_{46} & a_{47} & a_{48} & a_{49} & a_{4,10} & a_{4,11} & a_{4,12} & a_{4,13} & a_{4,14} & a_{4,15} & a_{4,16} \\
&  &  &  & a_{56} & a_{57} & a_{58} & a_{59} & a_{5,10} & a_{5,11} & a_{5,12} & a_{5,13} & a_{5,14} & a_{5,15} & a_{5,16} \\
&  &  &  &  & a_{67} & a_{68} & a_{69} & a_{6,10} & a_{6,11} & a_{6,12} & a_{6,13} & a_{6,14} & a_{6,15} & a_{6,16} \\
 &  &  &  &  &  & a_{78} & a_{79} & a_{7,10} & a_{7,11} & a_{7,12} & a_{7,13} & a_{7,14} & a_{7,15} & a_{7,16} \\
 &  &  &  &  &  &  & a_{89} & a_{8,10} & a_{8,11} & a_{8,12} & a_{8,13} & a_{8,14} & a_{8,15} & a_{8,16} \\
&  &  &  &  &  &  &  & a_{9,10} & a_{9,11} & a_{9,12} & a_{9,13} & a_{9,14} & a_{9,15} & a_{9,16} \\
&  &  &  &  &  &  &  &  & a_{10,11} & a_{10,12} & a_{10,13} & a_{10,14} & a_{10,15} & a_{10,16} \\
&  &  &  &  &  &  &  &  &  & a_{11,12} & a_{11,13} & a_{11,14} & a_{11,15} & a_{11,16} \\
&  &  &  &  &  &  &  &  &  &  & a_{12,13} & a_{12,14} & a_{12,15} & a_{12,16} \\
&  &  &  &  &  &  &  &  &  &  &  & a_{13,14} & a_{13,15} & a_{13,16} \\
&  &  &  &  &  &  &  &  &  &  &  &  & a_{14,15} & a_{14,16} \\
&  &  &  &  &  &  &  &  &  &  &  &  &  & a_{15,16} \\
\end{matrix}
\right)
\]

\end{document}

enter image description here

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