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Quantum Griffiths Effects In Itinerant Heisenberg Magnets, Thomas Vojta, Jörg Schmalian
Quantum Griffiths Effects In Itinerant Heisenberg Magnets, Thomas Vojta, Jörg Schmalian
Physics Faculty Research & Creative Works
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 …
Critical Behavior And Griffiths Effects In The Disordered Contact Process, Thomas Vojta, Mark Dickison
Critical Behavior And Griffiths Effects In The Disordered Contact Process, Thomas Vojta, Mark Dickison
Physics Faculty Research & Creative Works
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 109 and system sizes up to 107 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 104 or larger. In the Griffiths region between the clean and the dirty critical points, we …