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:2206.03363 · Physical review. E

Random-bond antiferromagnetic Ising model in a field

Jean-Christian Anglès d’Auriac, Ferenc Iglói

Published Sep 12, 2022• 0 citations
arXivHTMLPDF

Abstract

Using combinatorial optimization techniques we study the critical properties of the two- and three-dimensional Ising models with uniformly distributed random antiferromagnetic couplings $(1\ensuremath{\le}{J}_{i}\ensuremath{\le}2)$ in the presence of a homogeneous longitudinal field, $h$, at zero temperature. In finite systems of linear size, $L$, we measure the average correlation function, ${C}_{L}(\ensuremath{\ell},h)$, when the sites are either on the same sublattice, or they belong to different sublattices. The phase transition, which is of first order in the pure system, turns to mixed order in two dimensions with critical exponents $1/\ensuremath{\nu}\ensuremath{\approx}0.5$ and $\ensuremath{\eta}\ensuremath{\approx}0.7$. In three dimensions we obtain $1/\ensuremath{\nu}\ensuremath{\approx}0.7$, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.

DOI
10.1103/physreve.106.034117

Related papers

Reentrant random quantum Ising antiferromagnet

Péter Lajkó, Jean-Christian Anglès d’Auriac, Heiko Rieger +1 more

We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1\ensuremath{\le}{J}_{i}\ensuremath{\le}2)$ and uniformly distributed random transverse fields $({\mathrm{\ensuremath{\Gamma}}}_{0}\ensuremath{\le}{\mathrm{\ensuremath{\Gamma}}}_{i}\ensuremath{\le}2{\mathrm{\ensuremath{\Gamma}}}_{0})$ in the presence of a homogeneous longitudinal field, $h$. Using different numerical techniques (density-matrix renormalization group, combinatorial optimization, and strong disorder renormalization group methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line $(h=0,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=1)$ there is an infinite disorder quantum fixed point, while at the other end $(h=2,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=0)$ there is a classical random first-order transition point. Close to this fixed point, for $h>2$ and ${\mathrm{\ensuremath{\Gamma}}}_{0}>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.

arXiv:1912.06035•Physical review. B./Physical review. B•Jan 30, 2020•9 citations

Random-field Ising model: Insight from zero-temperature simulations

Panagiotis E. Theodorakis, Nikolaos G. Fytas

We enlighten some critical aspects of the three-dimensional (d = 3) random-field Ising model from simulations performed at zero temperature.We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model.By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes V = L × L × L, where L denotes linear lattice size and L max = 156.Using as finite-size measures the sampleto-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field h c and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class.Additional simulations of the Gaussian random-field Ising model at the best-known value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat.Finally, we discuss the infinite-limit size extrapolation of energyand order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.

arXiv:1501.02338•Condensed Matter Physics•Dec 1, 2014•9 citations

Phase diagrams of the ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model under a longitudinal magnetic field

N. Hachem, M Alehyane, Amer Lafhal +4 more

Abstract The ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field interaction in the absence and presence of a longitudinal magnetic field on a three-dimensional cubic lattice is studied within the framework both of the mean-field approximation (MFA) and Monte Carlo simulation (MCS). Using the MFA, we have shown the phase diagram of the model for zero magnetic field in the (anisotropy, temperature) plane in which the system exhibits first- and second-order phase transitions and critical end-points. Also, we have used the standard MCS to confirm the previous results; we have presented the temperature dependence of the sublattice and total magnetizations for different values of anisotropy in order to determine the phase diagram of the model in the absence of a longitudinal magnetic field. In addition, the influence of this last field on the magnetic properties of the model is investigated and discussed.

Physica Scripta•Nov 30, 2018•22 citations

Exact ground states of one-dimensional long-range random-field Ising magnets

Timo Dewenter, Alexander K. Hartmann

We investigate the one-dimensional long-range random-field Ising magnet with Gaussian distribution of the random fields. In this model, a ferromagnetic bond between two spins is placed with a probability $p\ensuremath{\sim}{r}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\sigma}}$, where $r$ is the distance between these spins and $\ensuremath{\sigma}$ is a parameter to control the effective dimension of the model. Exact ground states at zero temperature are calculated for system sizes up to $L={2}^{19}$ via graph theoretical algorithms for four different values of $\ensuremath{\sigma}\ensuremath{\in}{0.25,0.4,0.5,1.0}$ while varying the strength $h$ of the random fields. For each of these values several independent physical observables are calculated, i.e., magnetization, Binder parameter, susceptibility, and a specific-heat-like quantity. The ferromagnet-paramagnet transitions at critical values ${h}_{c}(\ensuremath{\sigma})$ as well as the corresponding critical exponents are obtained. The results agree well with theory, and interestingly we find for $\ensuremath{\sigma}=1/2$ the data is compatible with a critical random-field strength ${h}_{c}>0$.

arXiv:1307.3987•Physical Review B•Jul 31, 2014•10 citations

Mixed-order transition in the antiferromagnetic quantum Ising chain in a field

Péter Lajkó, Ferenc Iglói

The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first order for $h/\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}\ensuremath{\infty}, \mathrm{\ensuremath{\Gamma}}$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\mathrm{\ensuremath{\Gamma}}>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\mathrm{\ensuremath{\Gamma}}$ the transition is of mixed order.

arXiv:2012.07470•Physical review. B./Physical review. B•May 4, 2021•9 citations

Fluctuations and criticality in the random-field Ising model

Panagiotis E. Theodorakis, Ioannis Georgiou, Nikolaos G. Fytas

We investigate the critical properties of the $d=3$ random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength $h$ and system sizes $\mathcal{V}=L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$, with $L\ensuremath{\le}156$. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength ${h}_{\mathrm{c}}$ and the correlation length exponent $\ensuremath{\nu}$. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent $\ensuremath{\alpha}$ and the violation of the hyperscaling exponent $\ensuremath{\theta}$. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios $\ensuremath{\beta}/\ensuremath{\nu}$ and $\overline{\ensuremath{\gamma}}/\ensuremath{\nu}$, respectively.

Physical Review E•Mar 8, 2013•11 citations
Using combinatorial optimization techniques we study the critical properties of the two- and three-dimensional Ising models with uniformly distributed random antiferromagnetic couplings (1\ensuremath≤Ji\ensuremath≤2)(1\ensuremath{\le}{J}_{i}\ensuremath{\le}2)(1\ensuremath≤Ji​\ensuremath≤2) in the presence of a homogeneous longitudinal field, hhh, at zero temperature. In finite systems of linear size, LLL, we measure the average correlation function, CL(\ensuremathℓ,h){C}_{L}(\ensuremath{\ell},h)CL​(\ensuremathℓ,h), when the sites are either on the same sublattice, or they belong to different sublattices. The phase transition, which is of first order in the pure system, turns to mixed order in two dimensions with critical exponents 1/\ensuremathν\ensuremath≈0.51/\ensuremath{\nu}\ensuremath{\approx}0.51/\ensuremathν\ensuremath≈0.5 and \ensuremathη\ensuremath≈0.7\ensuremath{\eta}\ensuremath{\approx}0.7\ensuremathη\ensuremath≈0.7. In three dimensions we obtain 1/\ensuremathν\ensuremath≈0.71/\ensuremath{\nu}\ensuremath{\approx}0.71/\ensuremathν\ensuremath≈0.7, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.
We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1\ensuremath{\le}{J}_{i}\ensuremath{\le}2)$ and uniformly distributed random transverse fields $({\mathrm{\ensuremath{\Gamma}}}_{0}\ensuremath{\le}{\mathrm{\ensuremath{\Gamma}}}_{i}\ensuremath{\le}2{\mathrm{\ensuremath{\Gamma}}}_{0})$ in the presence of a homogeneous longitudinal field, hhh. Using different numerical techniques (density-matrix renormalization group, combinatorial optimization, and strong disorder renormalization group methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line $(h=0,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=1)$ there is an infinite disorder quantum fixed point, while at the other end $(h=2,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=0)$ there is a classical random first-order transition point. Close to this fixed point, for h>2h>2h>2 and ${\mathrm{\ensuremath{\Gamma}}}_{0}>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.
We enlighten some critical aspects of the three-dimensional (d = 3) random-field Ising model from simulations performed at zero temperature.We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model.By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes V = L × L × L, where L denotes linear lattice size and L max = 156.Using as finite-size measures the sampleto-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field h c and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class.Additional simulations of the Gaussian random-field Ising model at the best-known value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat.Finally, we discuss the infinite-limit size extrapolation of energyand order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.
Abstract The ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field interaction in the absence and presence of a longitudinal magnetic field on a three-dimensional cubic lattice is studied within the framework both of the mean-field approximation (MFA) and Monte Carlo simulation (MCS). Using the MFA, we have shown the phase diagram of the model for zero magnetic field in the (anisotropy, temperature) plane in which the system exhibits first- and second-order phase transitions and critical end-points. Also, we have used the standard MCS to confirm the previous results; we have presented the temperature dependence of the sublattice and total magnetizations for different values of anisotropy in order to determine the phase diagram of the model in the absence of a longitudinal magnetic field. In addition, the influence of this last field on the magnetic properties of the model is investigated and discussed.
We investigate the one-dimensional long-range random-field Ising magnet with Gaussian distribution of the random fields. In this model, a ferromagnetic bond between two spins is placed with a probability $p\ensuremath{\sim}{r}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\sigma}}$, where rrr is the distance between these spins and $\ensuremath{\sigma}$ is a parameter to control the effective dimension of the model. Exact ground states at zero temperature are calculated for system sizes up to L=219L={2}^{19}L=219 via graph theoretical algorithms for four different values of $\ensuremath{\sigma}\ensuremath{\in}{0.25,0.4,0.5,1.0}$ while varying the strength hhh of the random fields. For each of these values several independent physical observables are calculated, i.e., magnetization, Binder parameter, susceptibility, and a specific-heat-like quantity. The ferromagnet-paramagnet transitions at critical values ${h}_{c}(\ensuremath{\sigma})$ as well as the corresponding critical exponents are obtained. The results agree well with theory, and interestingly we find for $\ensuremath{\sigma}=1/2$ the data is compatible with a critical random-field strength hc>0{h}_{c}>0hc​>0.
The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field (hhh) is switched on, the phase transition is preserved, which turns to first order for $h/\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}\ensuremath{\infty}, \mathrm{\ensuremath{\Gamma}}$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\mathrm{\ensuremath{\Gamma}}>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\mathrm{\ensuremath{\Gamma}}$ the transition is of mixed order.
We investigate the critical properties of the d=3d=3d=3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength hhh and system sizes $\mathcal{V}=L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$, with $L\ensuremath{\le}156$. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength hc{h}_{\mathrm{c}}hc​ and the correlation length exponent $\ensuremath{\nu}$. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent $\ensuremath{\alpha}$ and the violation of the hyperscaling exponent $\ensuremath{\theta}$. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios $\ensuremath{\beta}/\ensuremath{\nu}$ and $\overline{\ensuremath{\gamma}}/\ensuremath{\nu}$, respectively.