Solution
= Solution
Mean field replaces edge and triangle products by $m^2$ and $m^3$. There are $3N$ edges and $2N$ elementary triangles, so
$$
\boxed{Z_N\simeq\sum_M\binom{N}{(N+M)/2}\exp\{\beta N(Bm+3Jm^2+2Km^3)\}.}
$$
= Solution
Mean field replaces edge and triangle products by $m^2$ and $m^3$. There are $3N$ edges and $2N$ elementary triangles, so
$$
\boxed{Z_N\simeq\sum_M\binom{N}{(N+M)/2}\exp\{\beta N(Bm+3Jm^2+2Km^3)\}.}
$$