Criticality found in a model for orientational ordering of protein arrays.

MC-PSRG analysis allowed us to reduce criticalities A, B, and C found in the poker chip model, respectively, to ones of the Ising universality, of the 3-state Potts universality, and of the KT-like phase. We note that not only the KT-like phase but also the Ising and 3-state Potts universality have been predicted to appear in the generalized 6-state clock model. We expect that the criticality inherent in actual protein array systems, whose Hamiltonians might be more complex than those of the poker chip model, can also be reduced to the criticality clarified with the aid of the naive models. However, we have to direct our attention to nonuniversal behavior like criticality C. Several two-dimensional systems having the two-component order parameter exhibit nonuniversal critical behavior, whose critical exponents do not coincide with those for the XY model despite a coincidence in the number of order parameter components (17, 20, 25).