Study of phase transitions in Ising systems by exact microcanonical analysis

Ising chains and lattices have been studied excessively by canonical statistical analysis. Whereas there is no transition for 1D Ising chains, a ferromagnetic/paramagnetic phase transition occurs in 2D. In our study, we analyzed Ising chains, strips, and squares from the microcanonical perspective. The recently developed least-sensitive inflection-point method [1] was employed to identify potential transition signals in these systems [2, 3]. Our analysis confirms that there is no transition signal for 1D Ising chains as expected, but we find higher-order transitions in addition to the known second-order transition in the 2D Ising systems. A detailed cluster analysis lends insight into the nature of a third-order transition in the paramagnetic phase, which can be understood as a precursor of the continuous transition in the disordered phase.


[1] K. Qi and M. Bachmann, Phys. Rev. Lett. 120, 180601 (2018).
[2] K. Sitarachu, R. K. P. Zia, and M. Bachmann, J. Stat. Mech. 2020, 073204 (2020).
[3] K. Sitarachu and M. Bachmann, J. Phys: Conf. Ser. 1483, 012009 (2020).
(Proceedings of the Xth Brazilian Meeting on Statistical Physics, July 15-19, 2019, Belo Horizonte, Brazil)