Triplon condensation field scaling
= Triplon condensation field scaling
{title2=$H_c-H_g\propto T^{3/2}$}
For a three-dimensional quadratic branch, the critical thermal <density> is $n_T=\zeta(3/2)[mk_BT/(2\pi\hbar^2)]^{3/2}$. Inserting this into the mean-field gap-closing condition gives $H_c(T)-H_g=(\nu/\eta)n_T\propto T^{3/2}$. This is a dilute low-temperature model; finite bandwidth, anisotropy and changes in interactions can alter its applicability outside that regime.