Heisenberg Spin exchange figure with Tikz

Question

I want to construct a figure with Tikz similar to this one:

I was looking for example but couldn't find any I tried to make it but it was a mess.
so: How can I get the spins on the dots? and how to put them in a table while still being a tikz figure?
Thank you for your valuable help

Juan Castaño · Accepted Answer

With a tabular environment and a tikz newcommand you can do the following:
documentclass[border=2mm]{standalone}
usepackage{ifthen}
usepackage{tikz}

newcommand{level}[3]% up (1)/down (0), up (1)/down (0), labels (y/n)
{
  begin{tikzpicture}
    useasboundingbox (0,-0.25) rectangle (2,1.25);
    draw[blue,thick,-latex] (0,1-#1) -- (0,#1);
    draw[red ,thick,-latex] (2,1-#2) -- (2,#2);
    draw[dashed] (0,0.5)  -- (2,0.5);
    fill (0,0.5) circle (2pt);
    fill (2,0.5) circle (2pt);
    ifthenelse
      {equal{#3}{y}}
      {%
         node at (0,0)   [below] {$S_i$};
         node at (2,0)   [below] {$S_j$};
         node at (1,0.5) [above] {$J_{ij}$};
      }
      {}
   end{tikzpicture}
}

renewcommand{arraystretch}{2}
begin{document}
begin{tabular}{|c|c|}cline{1-2}
bfseries State 1 & bfseries State 2 hline
level{1}{1}{y}   & level{1}{0}{n}   hline
bfseries State 3 & bfseries State 4 hline
level{0}{1}{n}   & level{0}{0}{n}   hline
multicolumn{2}{|c|}{$displaystyle J_{ij}=frac{E_1+E_4-E_3-E_2}{4|S_iS_j|}$}[2mm]hline
end{tabular}
end{document}
[![enter image description here][1]][1]

[1]: https://i.stack.imgur.com/XGc5e.png

ubuntuuser · Answer

Maybe you can do this without tikz in a usual table using constructions as this one:
documentclass{article}
defqeq{mathrel{%
    mathchoice{QEQ}{QEQ}{scriptsizeQEQ}{tinyQEQ}%
}}
defQEQ{{%
    setbox0hbox{textbullet}%
    rlap{hbox to wd0{hss$uparrow$hss}}box0
}}

begin{document}

$qeq$ textbullet , textbullet , textbullet

end{document}

leandriis · Answer

documentclass{article}
usepackage{array}
usepackage{makecell}
usepackage{amsmath}
usepackage{tikz}
usetikzlibrary{positioning, arrows.meta}

tikzset{node distance = 1cm, baseline={(0,0)}}

newcommand{spinup}[1][]{
    draw[-Triangle , draw=#1, very thick] (0,0ex) -- (0ex,2em) node (up) {};
    draw[fill=black, draw=#1, draw=black] (0ex,1em) circle (0.5ex);
} % inspired by https://tex.stackexchange.com/a/314648/134144

newcommand{spindown}[1][]{
    draw[Triangle-, draw=#1, very thick] (0,0ex) -- (0ex,2em)node (down) {};
    draw[fill=black, draw=#1, draw=black] (0ex,1em) circle (0.5ex);
}

newcommand{energylevel}{draw [dotted] (0,0.9em) -- (1cm, 0.9em);}

setcellgapes{3pt}
begin{document}

makegapedcells
begin{tabular}{|wc{2cm}|wc{2cm}|}
hline
State 1 & State 2 
hline
begin{tikzpicture}
  energylevel;
  node at (0.5cm,2em) {$J_{ij}$};
  spinup[blue];
  node[below of = up]{$S_i$};
  spinup[red, right of= up]
  node[below of = up]{$S_j$};
end{tikzpicture}
& 
begin{tikzpicture}
  spinup[blue];
  spindown[red, right of= up];
  energylevel
end{tikzpicture}

hline
State 3 & State 4 
hline
begin{tikzpicture}
  energylevel;
  spindown[blue];
  spinup[red, right of= down]
end{tikzpicture}
& 
begin{tikzpicture}
  spindown[blue];
  spindown[red, right of= down];
  energylevel
end{tikzpicture}

hline
multicolumn{2}{|c|}{(displaystyle J_{ij} = frac{E_1 + E_4 - E_3 - E_2}{4 | S_i S_j |} )}
hline
end{tabular}

end{document}

Heisenberg Spin exchange figure with Tikz

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