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:2008.01464 · Physical review. B./Physical review. B

Universality in the three-dimensional random bond quantum Heisenberg antiferromagnet

Ulvi Kanbur, Erol Vatansever, Hamza Polat

Published Aug 14, 2020• 6 citations
arXivHTMLPDF

Abstract

The three-dimensional quenched random bond diluted $({J}_{1}\ensuremath{-}{J}_{2})$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ lattice up to $L=48$. By employing a standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio $r={J}_{2}/{J}_{1}$. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional $O(3)$ Heisenberg universality class.

DOI
10.1103/physrevb.102.064411

Related papers

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 behavior of three-dimensional Ising spin glass models

Martin Hasenbusch B, Andrea Pelissetto C, Ettore Vicari

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size $L$: the $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model for two values of the disorder parameter $p$, $p=0.5$ and $p=0.7$ (up to $L=28$ and $L=20$, respectively), and the bond-diluted bimodal model for bond-occupation probability ${p}_{b}=0.45$ (up to $L=16$). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent $\ensuremath{\omega}$ related to the leading irrelevant operator: $\ensuremath{\omega}=1.0(1)$. Shorter Monte Carlo simulations of the bond-diluted bimodal models at ${p}_{b}=0.7$ and ${p}_{b}=0.35$ (up to $L=10$) and of the Ising spin glass model with Gaussian bond distribution (up to $L=8$) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain $\ensuremath{\nu}=2.45(15)$ and $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.

arXiv:0809.3329•Physical Review B•Dec 17, 2008•119 citations

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

Massimo Campostrini B, Martin Hasenbusch B, Andrea Pelissetto C +2 more

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find $\ensuremath{\gamma}=1.3960(9),$ $\ensuremath{\nu}=0.7112(5),$ $\ensuremath{\eta}=0.0375(5),$ $\ensuremath{\alpha}=\ensuremath{-}0.1336(15),$ $\ensuremath{\beta}=0.3689(3),$ and $\ensuremath{\delta}=4.783(3).$ We consider an improved lattice ${\ensuremath{\varphi}}^{4}$ Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the ${\ensuremath{\varphi}}^{4}$ improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.

arXiv:cond-mat/0110336•Physical review. B, Condensed matter•Apr 2, 2002•482 citations

High-accuracy Monte Carlo study of the three-dimensional classical Heisenberg ferromagnet

Pawel Peczak, Alan M. Ferrenberg, D. P. Landau

Using extensive Monte Carlo simulations, we study the equilibrium properties of the simple-cubic, classical Heisenberg ferromagnet. We employ very long runs for L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L lattices to obtain high-precision data for the magnetization probability distribution. Using finite-size scaling for L\ensuremath{\le}24 and an optimized multiple-histogram data analysis, we obtain an accurate value of the inverse critical temperature J/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$=0.6929\ifmmode\pm\else\textpm\fi{}0.0001, which is higher than previously accepted estimates. Calculated values of various static exponents are in excellent agreement with renormalization-group and \ensuremath{\epsilon}-expansion predictions.

Physical review. B, Condensed matter•Mar 1, 1991•286 citations

Quantum Phase Transition of Two-Dimensional Diluted Heisenberg Antiferromagnet

Synge Todo, Chitoshi Yasuda, Kiyoshi Katō +4 more

Quantum phase transition of site-diluted and bond-diluted Heisenberg antiferromagnets on square lattices is studied. By using the novel continuous-time loop algorithm, we perform quantum Monte Carlo simulations on quite larger lattices at extremely lower temperatures than the previous numerical studies. It is found that the antiferromagnetic long-range order at T = 0 persists so long as a cluster of magnetic sites percolates, that is, the critical concentration is equal to the classical percolation threshold, in both of the site-diluted and bond-diluted cases. Furthermore, we find that some critical exponents, such as the magnetization exponent β, are non-classical and strongly depend on the spin size S. On the other hand, we show that the correlation-length exponent ν is universal and is equal to the classical value (ν=4/3).

Progress of Theoretical Physics Supplement•Jan 1, 2000•2 citations

Three-dimensional randomly dilute Ising model: Monte Carlo results

Pasquale Calabrese, Víctor Martín-Mayor, Andrea Pelissetto C +1 more

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L3 with L< or =256. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining nu=0.683(3), eta=0.035(2), beta=0.3535(17), and alpha=-0.049(9), in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio R(+)(xi) that expresses the universality of the free-energy density per correlation volume. We find R(+)(xi)=0.2885(15).

arXiv:cond-mat/0306272•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 30, 2003•53 citations
The three-dimensional quenched random bond diluted (J1\ensuremath−J2)({J}_{1}\ensuremath{-}{J}_{2})(J1​\ensuremath−J2​) quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for an L\ifmmode×\else\texttimes\fiL\ifmmode×\else\texttimes\fiLL\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}LL\ifmmode×\else\texttimes\fiL\ifmmode×\else\texttimes\fiL lattice up to L=48L=48L=48. By employing a standard finite-size scaling method, the numerical values of the N'eel temperature are determined with high precision as a function of the coupling ratio r=J2/J1r={J}_{2}/{J}_{1}r=J2​/J1​. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional O(3)O(3)O(3) Heisenberg universality class.
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.
We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size LLL: the $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model for two values of the disorder parameter ppp, p=0.5p=0.5p=0.5 and p=0.7p=0.7p=0.7 (up to L=28L=28L=28 and L=20L=20L=20, respectively), and the bond-diluted bimodal model for bond-occupation probability pb=0.45{p}_{b}=0.45pb​=0.45 (up to L=16L=16L=16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent $\ensuremath{\omega}$ related to the leading irrelevant operator: $\ensuremath{\omega}=1.0(1)$. Shorter Monte Carlo simulations of the bond-diluted bimodal models at pb=0.7{p}_{b}=0.7pb​=0.7 and pb=0.35{p}_{b}=0.35pb​=0.35 (up to L=10L=10L=10) and of the Ising spin glass model with Gaussian bond distribution (up to L=8L=8L=8) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain $\ensuremath{\nu}=2.45(15)$ and $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.
We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find $\ensuremath{\gamma}=1.3960(9),$ $\ensuremath{\nu}=0.7112(5),$ $\ensuremath{\eta}=0.0375(5),$ $\ensuremath{\alpha}=\ensuremath{-}0.1336(15),$ $\ensuremath{\beta}=0.3689(3),$ and $\ensuremath{\delta}=4.783(3).$ We consider an improved lattice ${\ensuremath{\varphi}}^{4}$ Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the ${\ensuremath{\varphi}}^{4}$ improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.
Using extensive Monte Carlo simulations, we study the equilibrium properties of the simple-cubic, classical Heisenberg ferromagnet. We employ very long runs for L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L lattices to obtain high-precision data for the magnetization probability distribution. Using finite-size scaling for L\ensuremath{\le}24 and an optimized multiple-histogram data analysis, we obtain an accurate value of the inverse critical temperature J/kB{\mathit{k}}_{\mathit{B}}kB​Tc{\mathit{T}}_{\mathit{c}}Tc​=0.6929\ifmmode\pm\else\textpm\fi{}0.0001, which is higher than previously accepted estimates. Calculated values of various static exponents are in excellent agreement with renormalization-group and \ensuremath{\epsilon}-expansion predictions.
Quantum phase transition of site-diluted and bond-diluted Heisenberg antiferromagnets on square lattices is studied. By using the novel continuous-time loop algorithm, we perform quantum Monte Carlo simulations on quite larger lattices at extremely lower temperatures than the previous numerical studies. It is found that the antiferromagnetic long-range order at T = 0 persists so long as a cluster of magnetic sites percolates, that is, the critical concentration is equal to the classical percolation threshold, in both of the site-diluted and bond-diluted cases. Furthermore, we find that some critical exponents, such as the magnetization exponent β, are non-classical and strongly depend on the spin size S. On the other hand, we show that the correlation-length exponent ν is universal and is equal to the classical value (ν=4/3).
We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L3 with L< or =256. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining nu=0.683(3), eta=0.035(2), beta=0.3535(17), and alpha=-0.049(9), in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio R(+)(xi) that expresses the universality of the free-energy density per correlation volume. We find R(+)(xi)=0.2885(15).