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arXiv:cond-mat/9905047 · Physical review. B, Condensed matter

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

Rajesh Narayanan, Thomas Vojta, D. Belitz, T. R. Kirkpatrick

Published Oct 1, 1999• 20 citations

Abstract

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.

DOI: 10.1103/physrevb.60.10150

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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)

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.

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.

Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.

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 effects of quenched disorder on the quantum phase transition of itinerant Heisenberg antiferromagnets. To this end, we apply a strong-disorder renormalization group method to the order parameter field theory of the problem. We find that the overdamped dynamics of the magnetic modes leads to a non-perturbative infinite-randomness critical point with unconventional activated dynamical scaling. We also discuss extra complications due long-range RKKY interactions as well as experimental implications for heavy fermion materials and other systems.

The phase-ordering dynamics that results from domain coarsening is considered for itinerant quantum ferromagnets. The fluctuation effects that invalidate the Hertz theory of the quantum phase transition also affect the phase ordering. For a quench into the ordered phase, there appears a transient regime where the domain growth follows a different power law than in the classical case, and for asymptotically long times, the prefactor of the

{t}^{1∕2}

growth law has an anomalous magnetization dependence. A quench to the quantum critical point results in a growth law that is not a power-law function of time. Both phenomenological scaling arguments and renormalization-group arguments are given to derive these results, and estimates of experimentally relevant length and time scales are presented.