TikZ: Using Loop to Draw Grid of Nodes

Question

I am trying to draw an Ising model (in my case, a grid of nodes with an undirected edge between adjacent nodes on the same row or column) using TikZ. I have the grid of nodes working nicely using a foreach loop, but I am having trouble drawing the lines between nodes. The problem lies in the fact that I am getting a syntax error when I try to \draw lines between computed node names.

Here is what I have so far:

Here is the code I am using:

\documentclass{minimal}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\scriptsize
\foreach \i in {1,...,25}
{
        \pgfmathtruncatemacro{\y}{(\i - 1) / 5};
        \pgfmathtruncatemacro{\x}{\i - 5 * \y};
        \pgfmathtruncatemacro{\label}{\x + 5 * (4 - \y)};
        \node[circle,draw=black,fill=white!80!black,minimum size=20]
        (\label) at (1.5*\x,1.5*\y) {\label};
}
% These draw commands are working as intended.
\draw (1) -- (2);
\draw (1) -- (6);
\draw (6) -- (7);
\draw (7) -- (2);
% The loop, however, is not =(
%\foreach \x in {1,...,4}
%\foreach \y in {0,...,4}
%{
%       \pgfmathtruncatemacro{\cur}{\x + 5 * \y};
%       \pgfmathtruncatemacro{\next}{\cur + 1};
%       \draw (\cur) -- (\next);
%}
\end{tikzpicture}
\end{document}

Thank you very much for your help!

Answer 1

It's possible to use a minimum code

\documentclass{minimal}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[darkstyle/.style={circle,draw,fill=gray!40,minimum size=20}]
  \foreach \x in {0,...,4}
    \foreach \y in {0,...,4} 
       {\pgfmathtruncatemacro{\label}{\x - 5 *  \y +21}
       \node [darkstyle]  (\x\y) at (1.5*\x,1.5*\y) {\label};} 

  \foreach \x in {0,...,4}
    \foreach \y [count=\yi] in {0,...,3}  
      \draw (\x\y)--(\x\yi) (\y\x)--(\yi\x) ;

\end{tikzpicture}
\end{document}  

Only for information you can get the grid with tkz-berge

\documentclass[border=0.25cm]{standalone}
\usepackage{tkz-berge}

\begin{document}

 \begin{tikzpicture}
      \GraphInit[vstyle=Shade]
   \grGrid[Math,RA=2,RB=2]{5}{5}
 \end{tikzpicture}

\end{document} 

Answer 2

With your loop:

\foreach \x in {1,...,4}
\foreach \y in {0,...,4}
{
       \pgfmathtruncatemacro{\cur}{\x + 5* \y}
       \pgfmathtruncatemacro{\next}{\cur + 1}
       \draw (\cur) -- (\next);
}

you are actually drawing just horizontal lines. Thus, if I understood correctly the question, you need to draw vertical lines.

For simplicity I used another loop:

% Vertical connections
\foreach \start in {1,...,20}
{
    \pgfmathtruncatemacro{\down}{\start+5}
    \draw (\start) -- (\down);  
}

Here is the full code:

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{positioning}

\tikzset{darkstyle/.style={circle,draw,fill=gray!40}}
\begin{document}
\begin{tikzpicture}
\foreach \i in {1,...,25}
{
        \pgfmathtruncatemacro{\y}{(\i - 1) / 5}
        \pgfmathtruncatemacro{\x}{\i - 5 * \y}
        \pgfmathtruncatemacro{\label}{\x + 5 * (4 - \y)}
        \node[darkstyle,minimum size=20] (\label) at (1.5*\x,1.5*\y)
        {\label};
}

% Horizontal connections

\foreach \x in {1,...,4}
\foreach \y in {0,...,4}
{
       \pgfmathtruncatemacro{\cur}{\x + 5* \y}
       \pgfmathtruncatemacro{\next}{\cur + 1}
       \draw (\cur) -- (\next);
}

% Vertical connections
\foreach \start in {1,...,20}
{
    \pgfmathtruncatemacro{\down}{\start+5}
    \draw (\start) -- (\down);  
}

\end{tikzpicture}
\end{document}

The result is:

Answer 3

As this looks like a grid, you could also use one (and probably two nested foreach loops for the node generation):

\documentclass{standalone}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\draw[step=1.5,thick] (0,-6) grid (6,0);
\foreach \x in {0,...,4}
{   \foreach \y in {0,...,4}
    {   \pgfmathtruncatemacro{\nodelabel}{\x+\y*5+1}
        \node[circle,draw=black,fill=white!80!black,minimum size=20] (\nodelabel) at (1.5*\x,-1.5*\y) {\nodelabel};
    }
}
\end{tikzpicture}

\end{document}

Answer 4

You can let TikZ do the loops with the graphs library/\graph syntax and the subgraph Grid_n from the graphs.standard library.

If you want to alter specific edges without having to draw all of them manually, you can use the simple key and manually specify options to individual edges (or even remove them with -!-).

Code

\documentclass[tikz]{standalone}
\usetikzlibrary{graphs.standard}
\begin{document}
\tikz[x=+1.5cm, y=+1.5cm]
  \graph[
    grid placement,
    nodes={circle, draw=black, fill=white!80!black, minimum size=+20pt}
  ]{ subgraph Grid_n [n = 25] };
\end{document}

Output