Hard Hexagon Entropy Constant

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

$\displaystyle \kappa_1$	$\textstyle \equiv$	$\displaystyle 4^{-1} 3^{5/4} 11^{-5/12} c^{-2}$	(3)
$\displaystyle \kappa_2$	$\textstyle \equiv$	$\displaystyle [1-\sqrt{1-c}+\sqrt{2+c+2\sqrt{1+c+c^2}}\,]^2$	(4)
$\displaystyle \kappa_3$	$\textstyle \equiv$	$\displaystyle [-1-\sqrt{1-c}+\sqrt{2+c+2\sqrt{1+c+c^2}}\,]^2$	(5)
$\displaystyle \kappa_4$	$\textstyle \equiv$	$\displaystyle [\sqrt{1-a}+\sqrt{2+a+2\sqrt{1+a+a^2}}\,]^{-1/2}$	(6)
$\displaystyle a$	$\textstyle \equiv$	$\displaystyle -{\textstyle{124\over 363}} 11^{1/3}$	(7)
$\displaystyle b$	$\textstyle \equiv$	$\displaystyle {\textstyle{2501\over 11979}} 33^{1/2}$	(8)
$\displaystyle c$	$\textstyle \equiv$	$\displaystyle \{{\textstyle{1\over 4}}+{\textstyle{3\over 8}}a[(b+1)^{1/3}-(b-1)^{1/3}]\}^{1/3}.$	(9)