Qin, MP (reprint author), Chinese Acad Sci, Inst Phys, POB 603, Beijing 100190, Peoples R China.
[Qin, M. P.
; Xie, Z. Y.
; Chen, J.
; Yu, J. F.
; Zhao, H. H.
; Xiang, T.] Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China
; [Chen, Q. N.] Chinese Acad Sci, Inst Theoret Phys, Beijing 100190, Peoples R China
; [Normand, B.] Renmin Univ China, Dept Phys, Beijing 100872, Peoples R China
; [Xiang, T.] Collaborat Innovat Ctr Quantum Matter, Beijing, Peoples R China
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic q-state Potts models on different two-dimensional lattices and for all relevant values of q. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties (entropy, specific heat, magnetization, and susceptibility) giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical q(c), and double phase transitions.