Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2306.17015 · Physical review. E

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

Kedkanok Sitarachu, Michael Bachmann

Published Jul 25, 2022• 19 citations
arXivHTMLPDF

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.

DOI
10.1103/physreve.106.014134

Related papers

Phase Transitions in the Two-Dimensional Ising Model from the Microcanonical Perspective

Kedkanok Sitarachu, Michael Bachmann

Abstract The continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized microcanonical inflection-point analysis method to investigate the least-sensitive inflection points of the microcanonical entropy and its derivatives to identify transition signals. Surprisingly, this method reveals that there are potentially two additional transitions for the Ising system besides the critical transition.

arXiv:2005.02240•Journal of Physics Conference Series•Feb 1, 2020•10 citations

Pseudo Transitions in the Finite-Size Blume-Capel Model

Shi, Lei, Wei Liu, Li, Xiang +4 more

This article investigates the pseudo transitions of the Blume-Capel model on two-dimensional finite-size lattices. By employing the Wang-Landau sampling method and microcanonical inflection point analysis, we identified the positions of phase transitions as well as higher-order phase transitions. Through Metropolis sampling and canonical ensemble analysis, we determined the geometric characteristics of the system at these transition points. When the crystal field parameter $D$ exceeds 1.965, crossing the tricritical point, no third-order dependent phase transition is observed. However, a fourth-order independent transition was identified in the high-temperature region, and through Metropolis sampling analysis, a phase transition from the ordered paramagnetic phase to the disordered paramagnetic phase was confirmed, enhancing the phase diagram. Furthermore, the positions of the third-order phase transition obtained from both microcanonical and canonical analyses are consistent and mutually corroborative. We speculate that third-order dependent transitions vanish in the presence of strong first-order phase transitions.

arXiv:2411.01743•Nov 4, 2024•0 citations

Exact microcanonical statistical analysis of transition behavior in Ising chains and strips

Kedkanok Sitarachu, Royce K. P. Zia, Michael Bachmann

Abstract Recent analyses of least-sensitive inflection points in derivatives of the microcanonical entropy for the two-dimensional Ising model revealed higher-order transition signals in addition to the well-studied second-order ferromagnetic/paramagnetic phase transition. In this paper, we re-analyze the exact density of states for the one-dimensional Ising chain as well as the strips with widths/lengths of up to 64/1024 spins, in search of potential transition features. While some transitions begin to emerge as the strip width increases, none are found for the chain, as might be expected.

arXiv:2306.16994•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2020•19 citations

Pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices

Wei Liu, Fangfang Wang, Pengwei Sun +1 more

Abstract This article offers a detailed analysis of pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices. We carry out Wang–Landau sampling to obtain the density of states. Using microcanonical inflection-point analysis with microcanonical entropy, we obtain the order of the pseudo-phase transitions in the models. The microcanonical analysis results of the second-order transition for the Ising model and the first-order transition for the Baxter–Wu model are consistent with the traditional canonical results. In addition, the third-order transitions are found in both models, implying the universality of higher-order phase transitions.

arXiv:2203.06563•Journal of Statistical Mechanics Theory and Experiment•Sep 1, 2022•7 citations

Geometric properties of the additional third-order transitions in the two-dimensional Potts model

Wei Liu, Xin Zhang, Lei Shi +4 more

Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the q-state Potts model (for q≥3), using two geometric order parameters: isolated spins number and the average perimeter of clusters. Our results confirm that higher-order transitions exist in the Potts model, where the number of isolated spins reliably indicates third-order independent transitions. This signal persists regardless of the system's phase transition order, even at higher values of q. In contrast, the average perimeter of clusters, used as an order parameter for detecting third-order dependent transitions, shows that for q=6 and 8, the signal for third-order dependent transitions disappears, indicating its absence in systems undergoing first-order transitions. These findings are consistent with results from microcanonical inflection-point analysis, further validating the robustness of this approach.

arXiv:2411.00423•Physical review. E•May 20, 2025•2 citations

Study of the Two-Dimensional Anisotropic Ising Model with Competing Interactions in the Region of a Transition from the Ferromagnetic to Paramagnetic State

Akai Kurbanovich Murtazaev, Zhavrail G. Ibaev

Abstract The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase has been studied by the Monte Carlo method using the Wang–Landau algorithm. State density distributions have been obtained and the order parameters corresponding to different energies have been calculated. The temperature dependences of the thermodynamic parameters including the internal energy, magnetization, free energy, entropy, specific heat at constant magnetization, and Binder cumulants have been calculated. Using the Binder cumulant method and histogram analysis, it has been shown that a single second-order phase transition from the ferromagnetic to paramagnetic phase occurs at two exchange coupling constants ratios |J1/J| = 0.1 and 0.2 in the two-dimensional anisotropic next-nearest neighbor Ising model. The phase transition temperatures have been calculated. The main critical exponents have been determined using the finite-size scaling theory.

Journal of Experimental and Theoretical Physics•Jan 1, 2020•0 citations
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.
Abstract The continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized microcanonical inflection-point analysis method to investigate the least-sensitive inflection points of the microcanonical entropy and its derivatives to identify transition signals. Surprisingly, this method reveals that there are potentially two additional transitions for the Ising system besides the critical transition.
This article investigates the pseudo transitions of the Blume-Capel model on two-dimensional finite-size lattices. By employing the Wang-Landau sampling method and microcanonical inflection point analysis, we identified the positions of phase transitions as well as higher-order phase transitions. Through Metropolis sampling and canonical ensemble analysis, we determined the geometric characteristics of the system at these transition points. When the crystal field parameter DDD exceeds 1.965, crossing the tricritical point, no third-order dependent phase transition is observed. However, a fourth-order independent transition was identified in the high-temperature region, and through Metropolis sampling analysis, a phase transition from the ordered paramagnetic phase to the disordered paramagnetic phase was confirmed, enhancing the phase diagram. Furthermore, the positions of the third-order phase transition obtained from both microcanonical and canonical analyses are consistent and mutually corroborative. We speculate that third-order dependent transitions vanish in the presence of strong first-order phase transitions.
Abstract Recent analyses of least-sensitive inflection points in derivatives of the microcanonical entropy for the two-dimensional Ising model revealed higher-order transition signals in addition to the well-studied second-order ferromagnetic/paramagnetic phase transition. In this paper, we re-analyze the exact density of states for the one-dimensional Ising chain as well as the strips with widths/lengths of up to 64/1024 spins, in search of potential transition features. While some transitions begin to emerge as the strip width increases, none are found for the chain, as might be expected.
Abstract This article offers a detailed analysis of pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices. We carry out Wang–Landau sampling to obtain the density of states. Using microcanonical inflection-point analysis with microcanonical entropy, we obtain the order of the pseudo-phase transitions in the models. The microcanonical analysis results of the second-order transition for the Ising model and the first-order transition for the Baxter–Wu model are consistent with the traditional canonical results. In addition, the third-order transitions are found in both models, implying the universality of higher-order phase transitions.
Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the q-state Potts model (for q≥3), using two geometric order parameters: isolated spins number and the average perimeter of clusters. Our results confirm that higher-order transitions exist in the Potts model, where the number of isolated spins reliably indicates third-order independent transitions. This signal persists regardless of the system's phase transition order, even at higher values of q. In contrast, the average perimeter of clusters, used as an order parameter for detecting third-order dependent transitions, shows that for q=6 and 8, the signal for third-order dependent transitions disappears, indicating its absence in systems undergoing first-order transitions. These findings are consistent with results from microcanonical inflection-point analysis, further validating the robustness of this approach.
Abstract The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase has been studied by the Monte Carlo method using the Wang–Landau algorithm. State density distributions have been obtained and the order parameters corresponding to different energies have been calculated. The temperature dependences of the thermodynamic parameters including the internal energy, magnetization, free energy, entropy, specific heat at constant magnetization, and Binder cumulants have been calculated. Using the Binder cumulant method and histogram analysis, it has been shown that a single second-order phase transition from the ferromagnetic to paramagnetic phase occurs at two exchange coupling constants ratios |J1/J| = 0.1 and 0.2 in the two-dimensional anisotropic next-nearest neighbor Ising model. The phase transition temperatures have been calculated. The main critical exponents have been determined using the finite-size scaling theory.