Invisible States

Usually states in a spin model contribute to both energy and entropy, but it is possible (and even physically reasonable) to have "invisible" states which only contribute entropically. 

• D. A. Johnston and R. P. K. C. M. Ranasinghe, Potts Models with (17) Invisible States on Thin Graphs, J. Phys. A46 225001, (2013)

• N. Ananikian, N. Sh. Izmailyan, D. A. Johnston, R. Kenna and R. P. K. C. M. Ranasinghe, Potts models with invisible states on general Bethe lattices, J. Phys. A46 385002, (2013)