%  matrix and probabilities for the triangle lattice 
%
\begin{tabular}{ccc|ccc} 
\qquad &        &        & \multicolumn{2}{c}{Operations} & \qquad \\ 
\qquad & Energy & Config \qquad\qquad & 1  & 2   & \qquad \\ 
\hline
\qquad & $-J$ & 1 \qquad\qquad & $e^{-4\beta J}$ & $1-e^{-4\beta J}$ & \qquad \\
\qquad & $3J$ & 2 \qquad\qquad & 1               & 0                 & \qquad \\
\end{tabular}
