Evidence for additional third-order transitions in the two-dimensional Ising model

TL;DR

This study uses a novel microcanonical analysis method to identify and classify higher-order phase transitions in the 2D Ising model, revealing additional third-order transitions beyond the well-known second-order transition.

Contribution

It introduces the microcanonical inflection-point analysis to detect and classify higher-order phase transitions in the 2D Ising model, uncovering previously unreported third-order transitions.

Findings

Evidence for third-order transitions in the ferromagnetic phase.

Identification of a dependent third-order transition in the paramagnetic phase.

Analysis of spin clusters provides insight into the nature of these transitions.

Abstract

We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and in the thermodynamic limit. Exact results for the density of states, which were obtained by exact algorithmic computation, 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, but it remains separate from the critical point in the thermodynamic limit. For a deeper insight into the nature of these additional transitions, a detailed analysis of spin clusters is performed.