Theory of order-disorder transitions in the graphite intercalation compounds ${\mathrm{C}}_8$Cs, ${\mathrm{C}}_8$Rb, and ${\mathrm{C}}_6$Li

The order-disorder transitions in the stage-1 graphite intercalation compounds ${\mathrm{C}}_8$Cs, ${\mathrm{C}}_8$Rb, and ${\mathrm{C}}_6$Li are analyzed within a Landau-Ginzburg theory. The transitions are all found to be first order, but for different reasons: In ${\mathrm{C}}_8$Cs the Landau expansion includes third-order umklapp terms, whereas in ${\mathrm{C}}_8$Rb the ordered phase is stablized by sixth-order anisotropy terms. The transition in ${\mathrm{C}}_6$Li is described by the three-dimensional three-state Potts model, which also contains cubic invariants. Experiments are suggested to test the predictions.