Evidence for higher-order phase transitions in the two-dimensional Ising model

We employed the microcanonical inflection-point analysis method [1], which was introduced to identify and classify phase transitions in systems of any size, to study the 2D Ising model at various lattice sizes and in the thermodynamic limit [2]. Exact results for the density of states, obtained by algorithmic computation [3,4], provide evidence for higher-order transitions in addition to the well-studied second-order ferromagnetic-paramagnetic phase transition. An independent third-order phase transition is identified in the ferromagnetic phase, whereas another third-order transition resides in the paramagnetic phase. The latter is a dependent transition, i.e., it is inevitably associated with the critical transition. Detailed cluster analysis is performed to study the nature of the dependent transition, which can be interpreted as a precursor of the ferromagnetic-paramagnetic phase transition in the disordered phase. It is noteworthy that both higher-order transitions survive in the thermodynamic limit.

[1] K. Qi and M. Bachmann, Phys. Rev. Lett.?120, 180601 (2018).

[2] K. Sitarachu and M. Bachmann, to be published.

[3] P. D. Beale, Phys. Rev. Lett. 76, 78 (1996).

[4] R. Häggkvist, A. Rosengren, D. Andrén, P. Kundrotas, P. H. Lundow, and K. Markström, Phys. Rev. E 69, 046204 (2004).