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

Bulletin of the American Physical Society

Quantum phase transitions in the transverse Ising model with three-spin interactions

O. F. de Alcantara Bonfim, B. Boechat, J. Florencio

Published Mar 6, 2018• 0 citations
OpenAlex

Related papers

Quantum phase transitions in the transverse 1-D Ising model with four-spin interactions

O. F. de Alcantara Bonfim, J. Florencio

Bulletin of the American Physical Society•Mar 21, 2005•0 citations

Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions

O. F. de Alcantara Bonfim, J. Florencio

In this work we investigate the quantum phase transitions at zero temperature of the one-dimensional transverse Ising model with an extra term containing four-spin interactions. The competition between the energy couplings of the model leads to an interesting zero-temperature phase diagram. We use a modified Lanczos method to determine the ground state and the first excited state energies of the system, with sizes of up to 20 spins. We apply finite size scaling to the energy gap to obtain the boundary region where ferromagnetic to paramagnetic transition takes place. We also find the critical exponent associated with the correlation length. We find a degenerate $⟨3,1⟩$ phase region. The first-order transition boundary between this phase and the paramagnetic phase is determined by analyzing the behavior of the transverse spin susceptibility as the system moves from one region to the other.

Physical Review B•Oct 18, 2006•11 citations

Quantum Ising Phases and Transitions in Transverse Ising Models

Bikas K. Chakrabarti, Amit Dutta, Parongama Sen

Lecture notes in physics. M, Monographs•Jan 1, 1996•274 citations

Quantum Ising Phases and Transitions in Transverse Ising Models

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Lecture notes in physics•Dec 12, 2012•495 citations

Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field

Yun-Tong Yang, Fuzhou Chen, Hong‐Gang Luo

Abstract A uniform longitudinal field applied to the transverse Ising model (TIM) distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart. While the ground state of the latter shows no quantum phase transition (QPT), the ground state of the former exhibits rich phases: paramagnetic, antiferromagnetic, and possibly disordered phases. Although the first two are clearly identified, the existence of the disordered phase remains controversial. Here, we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction J , the transverse field h x and the longitudinal field h z , and uncover which patterns are responsible for these three competing energy scales, thereby determining the possible phases and the QPTs among them. The system size ranges from L = 8 to 128 and the transverse field h x is fixed at 1. Under these parameters, our results show the existence of the disordered phase. For a small h z , the system transitions from a disordered phase to an antiferromagnetic phase as J increases. For a large h z , the system undergoes two phase transitions: from paramagnetic to disordered, and then to antiferromagnetic phase. These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.

arXiv:2301.05040•Chinese Physics B•Oct 21, 2025•1 citation

Dissecting the quantum phase transition in the transverse Ising model

Yun-Tong Yang, Fuzhou Chen, Hong‐Gang Luo

Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well established through the renormalization-group theory, the microscopic nature of the phase transitions remains to be understood in a satisfactory way. For example, how does the interaction between particle/spins drive the system across distinct phases as parameters vary, and how do these particle/spins respond to parameter variations during this transition process? In this work, we investigate these questions through the paradigmatic example of quantum phase transitions (QPT) in the one-dimensional transverse Ising model (TIM). We first introduce 2L collective structures, referred to as patterns, for the TIM with L ferromagnetically interacting spins, and then analyze the contributions of these patterns to the system's states, e.g., the ground state, the first excited state, and so on, from which the analog of the QPT process between the disordered phase in the weakly coupling regime and the ferromagnetic phase in the strongly coupling regime is clearly identified at the interaction strength J_{c}=1. We systematically explore this process for small lattice sizes of L=6,8,10,12, whose ground-state energies are identical to those obtained by directly numerical exact diagonalization. Increasing the system size up to L=128, the actual QPT point located at J_{c}=1 in the thermodynamical limit is gradually approached. Our results show that the pattern picture is not only able to provide a microscopic process of phase transitions, but also of practical interest in analyzing analogues of QPT in diverse quantum simulation platforms.

arXiv:2212.12702•Physical review. E•Sep 10, 2025•4 citations
In this work we investigate the quantum phase transitions at zero temperature of the one-dimensional transverse Ising model with an extra term containing four-spin interactions. The competition between the energy couplings of the model leads to an interesting zero-temperature phase diagram. We use a modified Lanczos method to determine the ground state and the first excited state energies of the system, with sizes of up to 20 spins. We apply finite size scaling to the energy gap to obtain the boundary region where ferromagnetic to paramagnetic transition takes place. We also find the critical exponent associated with the correlation length. We find a degenerate ⟨3,1⟩⟨3,1⟩⟨3,1⟩ phase region. The first-order transition boundary between this phase and the paramagnetic phase is determined by analyzing the behavior of the transverse spin susceptibility as the system moves from one region to the other.
Abstract A uniform longitudinal field applied to the transverse Ising model (TIM) distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart. While the ground state of the latter shows no quantum phase transition (QPT), the ground state of the former exhibits rich phases: paramagnetic, antiferromagnetic, and possibly disordered phases. Although the first two are clearly identified, the existence of the disordered phase remains controversial. Here, we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction J , the transverse field h x and the longitudinal field h z , and uncover which patterns are responsible for these three competing energy scales, thereby determining the possible phases and the QPTs among them. The system size ranges from L = 8 to 128 and the transverse field h x is fixed at 1. Under these parameters, our results show the existence of the disordered phase. For a small h z , the system transitions from a disordered phase to an antiferromagnetic phase as J increases. For a large h z , the system undergoes two phase transitions: from paramagnetic to disordered, and then to antiferromagnetic phase. These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.
Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well established through the renormalization-group theory, the microscopic nature of the phase transitions remains to be understood in a satisfactory way. For example, how does the interaction between particle/spins drive the system across distinct phases as parameters vary, and how do these particle/spins respond to parameter variations during this transition process? In this work, we investigate these questions through the paradigmatic example of quantum phase transitions (QPT) in the one-dimensional transverse Ising model (TIM). We first introduce 2L collective structures, referred to as patterns, for the TIM with L ferromagnetically interacting spins, and then analyze the contributions of these patterns to the system's states, e.g., the ground state, the first excited state, and so on, from which the analog of the QPT process between the disordered phase in the weakly coupling regime and the ferromagnetic phase in the strongly coupling regime is clearly identified at the interaction strength J_{c}=1. We systematically explore this process for small lattice sizes of L=6,8,10,12, whose ground-state energies are identical to those obtained by directly numerical exact diagonalization. Increasing the system size up to L=128, the actual QPT point located at J_{c}=1 in the thermodynamical limit is gradually approached. Our results show that the pattern picture is not only able to provide a microscopic process of phase transitions, but also of practical interest in analyzing analogues of QPT in diverse quantum simulation platforms.