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:cond-mat/0109108 · Journal of Physics A Mathematical and General

Quantum phase transitions in theJ-J' Heisenberg andXYspin-½ antiferromagnets on a square lattice: finite-size scaling analysis

Piotr Tomczak, Johannes Richter

Published Aug 10, 2001• 15 citations
arXivHTMLPDF

Abstract

We investigate the critical parameters of an order-disorder quantum phase transition in the spin-½ J - J ' Heisenberg and XY antiferromagnets on a square lattice. Based on the excitation gaps calculated by the exact diagonalization technique for systems up to 32 spins and finite-size scaling analysis we estimate the critical couplings and exponents of the correlation length for both models. Our analysis confirms the universal critical behaviour of these quantum phase transitions: they belong to 3D O(3) and 3D O(2) universality classes, respectively.

DOI
10.1088/0305-4470/34/33/104

Related papers

Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

Munehisa Matsumoto, Chitoshi Yasuda, Synge Todo +1 more

The $S=1/2$ and $S=1$ two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for $S=1,$ we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.

arXiv:cond-mat/0107115•Physical review. B, Condensed matter•Nov 30, 2001•182 citations

Evidence for an Unconventional Universality Class from a Two-Dimensional Dimerized Quantum Heisenberg Model

S. C. Wenzel, L. Bogacz, Wolfhard Janke E

The two-dimensional $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\ensuremath{\alpha}={J}^{\ensuremath{'}}/J$. The critical point of the order-disorder quantum phase transition in the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model is determined as ${\ensuremath{\alpha}}_{c}=2.5196(2)$ by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.

arXiv:0805.2500•Physical Review Letters•Sep 19, 2008•88 citations

Critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

The critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors are investigated by a replica Monte-Carlo method. Using the finite-size scaling theory the static critical exponents of specific heat, ordering parameter, susceptibility, correlation radius as well as the Fisher exponent are calculated. An analysis of data is performed both with and without taking into account a correction to the finite-size scaling. It was found that in the model under consideration the second order phase transition is observed. It is shown that this model belongs to the new class of universality of critical behavior.

Low Temperature Physics•Dec 1, 2011•24 citations

Finite-size scaling in the transverse Ising model on a square lattice

C J Hamer

Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6×6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming universality with the three-dimensional classical Ising model. Critical amplitudes are also estimated for both the energy gap and the ground-state energy.

arXiv:cond-mat/0007063•Journal of Physics A Mathematical and General•Sep 13, 2000•39 citations

Quantum phase transition, universality, and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on a honeycomb lattice

Yizhen Huang, Bin Xi, Xi Chen +3 more

The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J>0 in the armchair direction and ferromagnetic interaction J^{'}<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q_{2} and spin stiffness ρ in two directions for various coupling ratios α=J^{'}/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point α_{c}=-0.93. Through the finite-size scaling analysis on Q_{2}, ρ_{x}, and ρ_{y}, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α. A phase diagram in the coupling ratio α-magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C(T) for different α's intersects precisely at one point, similar to that of liquid ^{3}He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q_{2}, ρ, and C(T) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.

arXiv:1606.02069•Physical review. E•Jun 6, 2016•15 citations

Finite-Size Scaling in the transverse Ising Model on a Square Lattice

C. J. Hamer

Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6x6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming universality with the three-dimensional classical Ising model. Critical amplitudes are also estimated for both the energy gap and the ground-state energy.

•Jan 1, 2000•16 citations
We investigate the critical parameters of an order-disorder quantum phase transition in the spin-½ J - J ' Heisenberg and XY antiferromagnets on a square lattice. Based on the excitation gaps calculated by the exact diagonalization technique for systems up to 32 spins and finite-size scaling analysis we estimate the critical couplings and exponents of the correlation length for both models. Our analysis confirms the universal critical behaviour of these quantum phase transitions: they belong to 3D O(3) and 3D O(2) universality classes, respectively.
The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
The two-dimensional $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\ensuremath{\alpha}={J}^{\ensuremath{'}}/J$. The critical point of the order-disorder quantum phase transition in the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model is determined as ${\ensuremath{\alpha}}_{c}=2.5196(2)$ by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.
The critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors are investigated by a replica Monte-Carlo method. Using the finite-size scaling theory the static critical exponents of specific heat, ordering parameter, susceptibility, correlation radius as well as the Fisher exponent are calculated. An analysis of data is performed both with and without taking into account a correction to the finite-size scaling. It was found that in the model under consideration the second order phase transition is observed. It is shown that this model belongs to the new class of universality of critical behavior.
The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J>0 in the armchair direction and ferromagnetic interaction J^{'}<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q_{2} and spin stiffness ρ in two directions for various coupling ratios α=J^{'}/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point α_{c}=-0.93. Through the finite-size scaling analysis on Q_{2}, ρ_{x}, and ρ_{y}, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α. A phase diagram in the coupling ratio α-magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C(T) for different α's intersects precisely at one point, similar to that of liquid ^{3}He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q_{2}, ρ, and C(T) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.