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/0007063 · Journal of Physics A Mathematical and General

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

C J Hamer

Published Sep 13, 2000• 39 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0305-4470/33/38/303

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, 2000•16 citations

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

Chris J. Hamer, Tobias Hövelborn, Michael Bachhuber

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.

Journal of Physics A Mathematical and General•Jan 1, 1999•12 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.

arXiv:cond-mat/0109108•Journal of Physics A Mathematical and General•Aug 10, 2001•15 citations

Critical behavior of the two-dimensional Ising model in a transverse field: A density-matrix renormalization calculation

M. S. L. du Croo de Jongh, J. M. J. van Leeuwen

We have adjusted the density-matrix renormalization method to handle two-dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground-state wave function. Combining the results obtained for system sizes up to $30\ifmmode\times\else\texttimes\fi{}6$ and finite-size scaling, we derive the phase-transition point and the critical exponent for the gap in the Ising model in a transverse field on a two-dimensional square lattice.

arXiv:cond-mat/9709103•Physical review. B, Condensed matter•Apr 1, 1998•65 citations

Finite-size scaling in the (2+1)D Ising model

Chris J. Hamer

Hamiltonian eigenvalues are calculated for the (2+1)D Ising model on lattices up to 5*5 sites. Finite-size scaling techniques are used to estimate the critical coupling x c =0.329+or-0.001, and index v=0.635+or-0.005. The prospects are discussed for further applications of these methods in three and four dimensions.

Journal of Physics A Mathematical and General•Apr 21, 1983•23 citations

Fidelity approach to quantum phase transitions: finite-size scaling for the quantum Ising model in a transverse field

Huan-Qiang Zhou, Jian-Hui Zhao, Bo Li

We analyze the fidelity per lattice site for two different ground states of the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the fidelity per lattice site is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite-size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.

arXiv:0704.2940•Journal of Physics A Mathematical and Theoretical•Oct 29, 2008•96 citations
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.
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 have adjusted the density-matrix renormalization method to handle two-dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground-state wave function. Combining the results obtained for system sizes up to $30\ifmmode\times\else\texttimes\fi{}6$ and finite-size scaling, we derive the phase-transition point and the critical exponent for the gap in the Ising model in a transverse field on a two-dimensional square lattice.
We analyze the fidelity per lattice site for two different ground states of the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the fidelity per lattice site is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite-size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.