The dilute Bose gas model used to analyse C ( T ) and M ( T ) around the QCP. The density of states D ( E ) for the 2D honeycomb tight-binding model has a bandwidth of 3 J and a finite value at E = 0, D = √3/2π J . In the presence of a small interlayer coupling J ⊥ (« J ), a 3D density of states with D ( E ) proportional to √ E shows up at the bottom of the band over the scale of J ⊥ . The effective chemical potential μ eff ( T ) = gμ B ( H s − H ) − 2 U eff < n > approaches E = 0 linearly with T at H = H s . For H < H s , μ eff goes to zero at a finite temperature due to the suppression of the logarithmic divergence by the 3D DOS below E c .
