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:2511.01661 · Annalen der Physik

Quantum Critical Behavior of Diluted Quasi‐One‐Dimensional Ising Chains

Logan Sowadski, Thomas Vojta

Published Dec 29, 2025• 0 citations
arXivHTMLPDF

Abstract

ABSTRACT is a unique magnetic material. It features bulk 3D magnetic order at low temperatures, but its quantum critical behavior in a magnetic field is well described by the 1D transverse‐field Ising universality class. This behavior is facilitated by the structural arrangement of magnetic ions in nearly isolated zig‐zag chains. In this work, we investigate the effect of random site dilution on the critical properties of such a quasi‐1D quantum Ising system. To this end, we introduce an anisotropic site‐diluted 3D transverse‐field Ising model. We find that site dilution leads to unconventional activated scaling behavior at the quantum phase transition. Interestingly, the critical exponents of the quantum critical point are in good agreement with those of the disordered 3D transverse‐field Ising universality class, despite the strong spatial anisotropy. We discuss the generality of our findings as well as implications for experiments.

DOI
10.1002/andp.202500564

Related papers

Quantum Monte Carlo study of the bond- and site-diluted transverse-field Ising model

Calvin Krämer, Max Hörmann, Kai Phillip Schmidt

We study the transverse-field Ising model on a square lattice with bond- and site-dilution at zero temperature by stochastic series expansion quantum Monte Carlo simulations. Tuning the transverse field $h$ and the dilution $p$, the quantum phase diagram of both models is explored. Both quantum phase diagrams show long-range order for small $h$ and small $p$. The ordered phase of each is separated from the disordered (quantum) Griffiths phase by second-order phase transitions on two critical lines touching at a multi-critical point. Using Binder ratios we locate quantum critical points with high accuracy. The order-parameter critical exponent $β$ and the average correlation-length exponent $ν_{\mathrm{av}}$ are determined along the critical lines and at the multi-critical points via finite-size scaling. We find three internally consistent sets of critical exponents and compare them with potentially connected universality classes. The quantum Griffiths phase in the vicinity of the phase transition lines is analyzed through the local susceptibility. Our results indicate that activated scaling occurs not only at the percolation transition, but also at the phase transition line for $p$ smaller than the percolation threshold $p_c$.

arXiv:2505.07627•Physical review. B./Physical review. B•Jul 8, 2025•1 citation

Critical behavior of random transverse-field Ising spin chains

Daniel S. Fisher

A real-space renormalization-group treatment of random transverse-field Ising spin chains that was introduced previously is developed and extensively analyzed. It yields results that are asymptotically exact in the critical region near the zero-temperature para-to-ferromagnetic quantum phase transition. In particular, the exact scaling function is obtained for the magnetization as a function of a uniform applied magnetic field and the distance to the critical point, and up to the solution of a linear ordinary differential equation whose solution can be exhaustively analyzed, the scaling function of the average spin-spin correlation function is also obtained. Thus more exact information is obtainable about the critical behavior for this random model than is known for the pure version which is equivalent to the two-dimensional Ising model. The basic reason for this is the extremely broad distribution of energy scales that occurs at low energies near the critical point of the random system. For the random chain the distribution of the magnetization of the first spin in a semi-infinite system is also studied and the results found to agree in the scaling limit with results of McCoy obtained from the exact solution of the closely related McCoy-Wu Ising model; this provides strong justification for the validity of the present approach. The singular properties of the weakly ordered and weakly disordered ``Griffiths' phases'' that occur at zero temperature near the critical point are also studied, as well as the behavior at low but nonzero temperature. Possible extensions of the results and general lessons drawn from them for other random systems are briefly discussed.

Physical review. B, Condensed matter•Mar 1, 1995•828 citations

Emergence of the three-dimensional diluted Ising model universality class in a mixture of two magnets

Juan Jesus Ruiz-Lorenzo, M. Dudka, Mariana Krasnytska +1 more

Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a nonmagnetic component, where some lattice sites are occupied by Ising spins, while others are nonmagnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a nonmagnetic component, but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length s and concentration c. In doing so, we analyze the effect of structural disorder per se without appealing to the presence of a nonmagnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters s and c. The impact of their interplay is a subject of detailed analysis.

arXiv:2411.16659•Physical review. E•Feb 18, 2025•1 citation

Antiferromagnetic Ising chain in a mixed transverse and longitudinal magnetic field

А. А. Овчинников, Д. В. Дмитриев, V. Ya. Krivnov +1 more

We have studied the antiferromagnetic Ising chain in a transverse magnetic field ${h}_{x}$ and uniform longitudinal field ${h}_{z}.$ Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in ${(h}_{x}{,h}_{z})$ plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in ${h}_{z}$ the scaling behavior of the mass gap in the vicinity of the critical point ${(h}_{x}{=1/2,h}_{z}=0)$ is established. It is found that the form of the transition line near the classical multicritical point ${(h}_{x}{=0,h}_{z}=1)$ is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.

arXiv:cond-mat/0306468•Physical review. B, Condensed matter•Dec 5, 2003•125 citations

Magnetic Grüneisen ratio of the random transverse‐field Ising chain

Thomas Vojta, José A. Hoyos

Abstract The magnetic analog of the Grüneisen parameter, that is, the magnetocaloric effect, is a valuable tool for studying field‐tuned quantum phase transitions. We determine the magnetic Grüneisen parameter of the one‐dimensional random transverse‐field Ising model, focusing on its low‐temperature behavior at the exotic infinite‐randomness quantum critical point and in the associated quantum Griffiths phases. We present extensive numerical simulations showing that the magnetic Grüneisen parameter diverges logarithmically with decreasing temperature in the quantum Griffiths phase. It changes sign right at criticality. These results confirm a recent strong‐disorder renormalization group theory. We also compare our findings to the behavior of the clean transverse‐field Ising chain.

arXiv:0906.0972•physica status solidi (b)•Feb 10, 2010•3 citations

Critical properties and phase diagram of quantum anisotropic XY spin chain in a random magnetic field: A density-matrix renormalization-group analysis

Aušrius Juozapavičius, Laura Urba, S. Caprara +1 more

The spin-1/2 quantum anisotropic $\mathrm{XY}$ spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.

Physical review. B, Condensed matter•Dec 1, 1999•11 citations
ABSTRACT is a unique magnetic material. It features bulk 3D magnetic order at low temperatures, but its quantum critical behavior in a magnetic field is well described by the 1D transverse‐field Ising universality class. This behavior is facilitated by the structural arrangement of magnetic ions in nearly isolated zig‐zag chains. In this work, we investigate the effect of random site dilution on the critical properties of such a quasi‐1D quantum Ising system. To this end, we introduce an anisotropic site‐diluted 3D transverse‐field Ising model. We find that site dilution leads to unconventional activated scaling behavior at the quantum phase transition. Interestingly, the critical exponents of the quantum critical point are in good agreement with those of the disordered 3D transverse‐field Ising universality class, despite the strong spatial anisotropy. We discuss the generality of our findings as well as implications for experiments.
We study the transverse-field Ising model on a square lattice with bond- and site-dilution at zero temperature by stochastic series expansion quantum Monte Carlo simulations. Tuning the transverse field hhh and the dilution ppp, the quantum phase diagram of both models is explored. Both quantum phase diagrams show long-range order for small hhh and small ppp. The ordered phase of each is separated from the disordered (quantum) Griffiths phase by second-order phase transitions on two critical lines touching at a multi-critical point. Using Binder ratios we locate quantum critical points with high accuracy. The order-parameter critical exponent βββ and the average correlation-length exponent νavν_{\mathrm{av}}νav​ are determined along the critical lines and at the multi-critical points via finite-size scaling. We find three internally consistent sets of critical exponents and compare them with potentially connected universality classes. The quantum Griffiths phase in the vicinity of the phase transition lines is analyzed through the local susceptibility. Our results indicate that activated scaling occurs not only at the percolation transition, but also at the phase transition line for ppp smaller than the percolation threshold pcp_cpc​.
A real-space renormalization-group treatment of random transverse-field Ising spin chains that was introduced previously is developed and extensively analyzed. It yields results that are asymptotically exact in the critical region near the zero-temperature para-to-ferromagnetic quantum phase transition. In particular, the exact scaling function is obtained for the magnetization as a function of a uniform applied magnetic field and the distance to the critical point, and up to the solution of a linear ordinary differential equation whose solution can be exhaustively analyzed, the scaling function of the average spin-spin correlation function is also obtained. Thus more exact information is obtainable about the critical behavior for this random model than is known for the pure version which is equivalent to the two-dimensional Ising model. The basic reason for this is the extremely broad distribution of energy scales that occurs at low energies near the critical point of the random system. For the random chain the distribution of the magnetization of the first spin in a semi-infinite system is also studied and the results found to agree in the scaling limit with results of McCoy obtained from the exact solution of the closely related McCoy-Wu Ising model; this provides strong justification for the validity of the present approach. The singular properties of the weakly ordered and weakly disordered ``Griffiths' phases'' that occur at zero temperature near the critical point are also studied, as well as the behavior at low but nonzero temperature. Possible extensions of the results and general lessons drawn from them for other random systems are briefly discussed.
Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a nonmagnetic component, where some lattice sites are occupied by Ising spins, while others are nonmagnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a nonmagnetic component, but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length s and concentration c. In doing so, we analyze the effect of structural disorder per se without appealing to the presence of a nonmagnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters s and c. The impact of their interplay is a subject of detailed analysis.
We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx{h}_{x}hx​ and uniform longitudinal field hz.{h}_{z}.hz​. Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in (hx,hz){(h}_{x}{,h}_{z})(hx​,hz​) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in hz{h}_{z}hz​ the scaling behavior of the mass gap in the vicinity of the critical point (hx=1/2,hz=0){(h}_{x}{=1/2,h}_{z}=0)(hx​=1/2,hz​=0) is established. It is found that the form of the transition line near the classical multicritical point (hx=0,hz=1){(h}_{x}{=0,h}_{z}=1)(hx​=0,hz​=1) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.
Abstract The magnetic analog of the Grüneisen parameter, that is, the magnetocaloric effect, is a valuable tool for studying field‐tuned quantum phase transitions. We determine the magnetic Grüneisen parameter of the one‐dimensional random transverse‐field Ising model, focusing on its low‐temperature behavior at the exotic infinite‐randomness quantum critical point and in the associated quantum Griffiths phases. We present extensive numerical simulations showing that the magnetic Grüneisen parameter diverges logarithmically with decreasing temperature in the quantum Griffiths phase. It changes sign right at criticality. These results confirm a recent strong‐disorder renormalization group theory. We also compare our findings to the behavior of the clean transverse‐field Ising chain.
The spin-1/2 quantum anisotropic XY\mathrm{XY}XY spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.