Journal of Physics A Mathematical and General

Finite-size scaling in the spin- model on a square lattice

Chris J. Hamer, Tobias Hövelborn, Michael Bachhuber

Published Jan 1, 1999• 12 citations

Abstract

Energy eigenvalues and order parameters are calculated by exact diagonalization for the isotropic spin- model on square lattices of up to sites. The finite-size scaling behaviour is in excellent agreement with the effective Lagrangian predictions of Hasenfratz and Niedermayer (Hasenfratz P and Niedermayer F 1993 Z. Phys. B 92 91). Estimates are obtained for the bulk ground-state energy per site, the spontaneous magnetization, the spin-wave velocity and the spin-wave stiffness.

DOI: 10.1088/0305-4470/32/1/007

Related papers

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, 200016 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/0007063Journal of Physics A Mathematical and GeneralSep 13, 200039 citations

1 The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N = 40 spins

Johannes Richter, J. Schulenburg

Jan 1, 200991 citations

Exact diagonalization and quantum Monte Carlo study of the spin- 12 XXZ model on the square lattice

Hua Lin, James Flynn, Donald D. Betts

Physical review. B, Condensed matterNov 8, 200123 citations

Direct calculation of the spin stiffness in the J1 - J2 Heisenberg antiferromagnet

Torbjörn Einarsson, Heinz J. Schulz

arXiv:cond-mat/9410090Physical review. B, Condensed matterMar 1, 199581 citations

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

Piotr Tomczak, Johannes Richter

arXiv:cond-mat/0109108Journal of Physics A Mathematical and GeneralAug 10, 200115 citations

Journal of Physics A Mathematical and General

Finite-size scaling in the spin- model on a square lattice

Chris J. Hamer, Tobias Hövelborn, Michael Bachhuber

Published Jan 1, 1999• 12 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/32/1/007

Related papers

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

C. J. Hamer

Jan 1, 200016 citations

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

C J Hamer

arXiv:cond-mat/0007063Journal of Physics A Mathematical and GeneralSep 13, 200039 citations

1 The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N = 40 spins

Johannes Richter, J. Schulenburg

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1

Jan 1, 200991 citations

Exact diagonalization and quantum Monte Carlo study of the spin- 12 XXZ model on the square lattice

Hua Lin, James Flynn, Donald D. Betts

The spin- $\frac{1}{2}$ $\mathrm{XXZ}$ model on an infinite square lattice at zero temperature has been studied and is presented here. Our methods using finite square lattices have been the exact diagonalization and quantum Monte Carlo methods. The physical properties estimated per lattice vertex include ground-state and first-excited-state energy, staggered magnetization, and susceptibility in the parallel and perpendicular directions, spin stiffness, and spin-wave velocity. In the $\mathrm{XXZ}$ model range from the Ising model to the Heisenberg model our estimates of physical properties compare very well with estimates by several other methods published in several other papers. In the $\mathrm{XXZ}$ range between the Heisenberg and $\mathrm{XY}$ models there is very little in the literature to compare with our finite lattice estimates of physical properties.The spin-$\frac{1}{2}$ $\mathrm{XXZ}$ model on an infinite square lattice at zero temperature has been studied and is presented here. Our methods using finite square lattices have been the exact diagonalization and quantum Monte Carlo methods. The physical properties estimated per lattice vertex include ground-state and first-excited-state energy, staggered magnetization, and susceptibility in the parallel and perpendicular directions, spin stiffness, and spin-wave velocity. In the $\mathrm{XXZ}$ model range from the Ising model to the Heisenberg model our estimates of physical properties compare very well with estimates by several other methods published in several other papers. In the $\mathrm{XXZ}$ range between the Heisenberg and $\mathrm{XY}$ models there is very little in the literature to compare with our finite lattice estimates of physical properties.

Physical review. B, Condensed matterNov 8, 200123 citations

Direct calculation of the spin stiffness in the J1 - J2 Heisenberg antiferromagnet

Torbjörn Einarsson, Heinz J. Schulz

We calculate the spin stiffness ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ for the frustrated spin-1/2 Heisenberg antiferromagnet on a square lattice by exact diagonalizations on finite clusters of up to 36 sites followed by extrapolations to the thermodynamic limit. For the nonfrustrated case, we find that ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$=(0.183\ifmmode\pm\else\textpm\fi{}0.003) ${\mathit{J}}_{1}$ , in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for 0.4\ensuremath{\lesssim} ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ \ensuremath{\lesssim}0.6. In this intermediate region, the finite-size scaling works poorly---an additional sign that there is neither N\'eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N\'eel-ordered region.We calculate the spin stiffness ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ for the frustrated spin-1/2 Heisenberg antiferromagnet on a square lattice by exact diagonalizations on finite clusters of up to 36 sites followed by extrapolations to the thermodynamic limit. For the nonfrustrated case, we find that ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$=(0.183\ifmmode\pm\else\textpm\fi{}0.003)${\mathit{J}}_{1}$, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for 0.4\ensuremath{\lesssim}${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\lesssim}0.6. In this intermediate region, the finite-size scaling works poorly---an additional sign that there is neither N\'eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N\'eel-ordered region.

arXiv:cond-mat/9410090Physical review. B, Condensed matterMar 1, 199581 citations

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

Piotr Tomczak, Johannes Richter

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.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.

arXiv:cond-mat/0109108Journal of Physics A Mathematical and GeneralAug 10, 200115 citations

The spin-

\frac{1}{2}

\mathrm{XXZ}

model on an infinite square lattice at zero temperature has been studied and is presented here. Our methods using finite square lattices have been the exact diagonalization and quantum Monte Carlo methods. The physical properties estimated per lattice vertex include ground-state and first-excited-state energy, staggered magnetization, and susceptibility in the parallel and perpendicular directions, spin stiffness, and spin-wave velocity. In the

\mathrm{XXZ}

model range from the Ising model to the Heisenberg model our estimates of physical properties compare very well with estimates by several other methods published in several other papers. In the

\mathrm{XXZ}

range between the Heisenberg and

\mathrm{XY}

models there is very little in the literature to compare with our finite lattice estimates of physical properties.

{\mathit{J}}_{1}

, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for 0.4\ensuremath{\lesssim}

{\mathit{J}}_{2}

{\mathit{J}}_{1}

\ensuremath{\lesssim}0.6. In this intermediate region, the finite-size scaling works poorly---an additional sign that there is neither N\'eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N\'eel-ordered region.