Critical temperature of the Ising ferromagnet on the fcc, hcp, and dhcp lattices

• First Ising critical temperatures calculated on the hcp and double hcp lattices.
• Ising critical temperature on the fcc lattice with unprecedented precision.
• The hcp lattice has higher critical temperature than the fcc and double hcp lattices.

By an extensive Monte-Carlo calculation together with the finite-size-scaling and the multiple histogram method, the critical coupling constant (Kc=J/kBTcKc=J/kBTc) of the Ising ferromagnet on the fcc, hcp, and double hcp (dhcp) lattices were obtained with unprecedented precision: Kcfcc=0.1020707(2), Kchcp=0.1020702(1), and Kcdhcp=0.1020706(2). The critical temperature TcTc of the hcp lattice is found to be higher than those of the fcc and the dhcp lattice. The dhcp lattice seems to have higher TcTc than the fcc lattice, but the difference is within error bars.