Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
Sandvik, Anders W.
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Citation (published version)Iino, S., Morita, S., Kawashima, N., & Sandvik, A. W. (2019). Detecting signals of weakly first-order phase transitions in two-dimensional Potts models. Journal of the Physical Society of Japan, 88(3), 034006. https://doi.org/10.7566/JPSJ.88.034006
We investigate the first-order phase transitions of the q-state Potts models with q = 5, 6, 7, and 8 on the two- dimensional square lattice, using Monte Carlo simulations. At the very weakly first-order transition of the q = 5 system, the standard data-collapse procedure for the order parameter, carried out with results for a broad range of system sizes, works deceptively well and produces non-trivial critical exponents different from the trivial values expected for first- order transitions. However, we show a more systematic study on the “pseudo-critical” exponents as a function of the system size signals first-order phase transitions. We also derive a novel scaling behavior of Binder ratio based on a phenomenological theory for first-order transitions, which can detect the weakly first-order transitions in much smaller lattices than the correlation lengths. The results overall show that proper care is indispensable to diagnose the nature of a phase transition with limited system sizes.