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/0004013 · Physical review. B, Condensed matter

Effect of rare locally ordered regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

Rajesh Narayanan, Thomas Vojta

Published Dec 11, 2000• 2 citations
arXivHTMLPDF

Abstract

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one-loop renormalization-group analysis of the effective action shows that for order-parameter dimensions $p<4,$ the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions $p>4,$ the critical behavior is not influenced by the rare regions; it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

DOI
10.1103/physrevb.63.014405

Related papers

Critical behavior of disordered quantum magnets: The relevance of rare regions

Rajesh Narayanan, Thomas Vojta, D. Belitz +1 more

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered nonperturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.

arXiv:cond-mat/9905047•Physical review. B, Condensed matter•Oct 1, 1999•20 citations

Quantum Griffiths effects in itinerant Heisenberg magnets

Thomas Vojta, Jörg Schmalian

We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the Landau damping of the spin fluctuations suppresses the tunneling of the rare regions, the Heisenberg system displays strong power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We discuss these phenomena based on general scaling arguments, and we illustrate them by an explicit calculation for $O(N)$ spin symmetry in the large-$N$ limit. We also discuss broad implications for the classification of quantum phase transitions in the presence of quenched disorder.

arXiv:cond-mat/0405609•Physical Review B•Jul 15, 2005•107 citations

Critical points and quenched disorder: From Harris criterion to rare regions and smearing

Thomas Vojta, Rastko Sknepnek

We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system.

•Jan 1, 2004•17 citations

Critical points and quenched disorder: From Harris criterion to rare regions and smearing

Thomas Vojta, Rastko Sknepnek

Abstract We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two‐dimensional model system. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

arXiv:cond-mat/0405070•physica status solidi (b)•Jun 22, 2004•16 citations

Critical behavior and Griffiths effects in the disordered contact process

Thomas Vojta, Mark E. Dickison

We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte Carlo simulations for times up to 10(9) and system sizes up to 10(7) sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of 10(4) or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder.

arXiv:cond-mat/0505354•Physical Review E•Sep 27, 2005•110 citations

Disorder-Induced Rounding of Certain Quantum Phase Transitions

Thomas Vojta

We study the influence of quenched disorder on quantum phase transitions in systems with overdamped dynamics. For Ising order-parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double-exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model system.

arXiv:cond-mat/0212305•Physical Review Letters•Mar 12, 2003•143 citations
We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one-loop renormalization-group analysis of the effective action shows that for order-parameter dimensions p<4,p<4,p<4, the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions p>4,p>4,p>4, the critical behavior is not influenced by the rare regions; it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.
The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered nonperturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.
We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the Landau damping of the spin fluctuations suppresses the tunneling of the rare regions, the Heisenberg system displays strong power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We discuss these phenomena based on general scaling arguments, and we illustrate them by an explicit calculation for O(N)O(N)O(N) spin symmetry in the large-NNN limit. We also discuss broad implications for the classification of quantum phase transitions in the presence of quenched disorder.
We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system.
Abstract We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two‐dimensional model system. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte Carlo simulations for times up to 10(9) and system sizes up to 10(7) sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of 10(4) or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder.
We study the influence of quenched disorder on quantum phase transitions in systems with overdamped dynamics. For Ising order-parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double-exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model system.