Random fields at a nonequilibrium phase transition

We investigate nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such "random-field" disorder is known to have dramatic effects: It prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we demonstrate that the phase transition of the one-dimensional generalized contact process persists in the presence of random field disorder. The dynamics in the symmetry-broken phase becomes ultraslow and is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by means of large-scale Monte-Carlo simulations.Comment: 5 pages, 4 eps figures included, final version as publishe

Random field disorder at an absorbing state transition in one and two dimensions

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems.Comment: 14.5 pages, 15 eps figures included. Longer version of arXiv:1206.1878 with many additional result

Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations

We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.Comment: 12 pages, 9 eps figures included, final version as publishe

Enhanced rare region effects in the contact process with long-range correlated disorder

We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally in the active phase while the bulk system is still in the inactive phase. Specifically, if the correlations decay as a power of the distance, the rare region probability is a stretched exponential of the rare region size rather than a simple exponential as is the case for uncorrelated disorder. As a result, the Griffiths singularities are enhanced and take a non-power-law form. The critical point itself is of infinite-randomness type but with critical exponent values that differ from the uncorrelated case. We report large-scale Monte-Carlo simulations that verify and illustrate our theory. We also discuss generalizations to higher dimensions and applications to other systems such as the random transverse-field Ising model, itinerant magnets and the superconductor-metal transition.Comment: 11 pages, 8 eps figures include

Unconventional phase transitions in random systems

In this thesis we study the effects of different types of disorder and quasiperiodic modulations on quantum, classical and nonequilibrium phase transitions. After a brief introduction, we examine the effect of topological disorder on phase transitions and explain a host of violations of the Harris and Imry-Ma criteria that predict the fate of disordered phase transitions. We identify a class of random and quasiperiodic lattices in which a topological constraint introduces strong anticorrelations leading to modifications of the Harris and Imry-Ma criteria for such lattices. We investigate whether or not the Imry-Ma criterion, that predicts that random field disorder destroys phase transitions in equilibrium systems in sufficiently low dimensions, also holds for nonequilibrium phase transitions. We find that the Imry-Ma criterion does not apply to a prototypical absorbing state nonequilibrium transition. In addition, we study the effect of disorder with long-range spatial correlations on the absorbing state phase transition in the contact process. Most importantly, we find that long-range correlations enhance the Griffiths singularities and change the universality class of the transition. We also investigate the absorbing state phase transition of the contact process with quasiperiodic transition rates using a real-space renormalization group which yields a complete theory of the resulting exotic infinite-modulation critical point. Moreover, we study the effect of quenched disorder on a randomly layered Heisenberg magnet by means of a large-scale Monte-Carlo simulations. We find that the transition follows the infinite-randomness critical point scenario. Finally, we investigate the effect of quenched disorder on the first-order phase transition in the N-color quantum Ashkin-Teller model by means of strong-disorder renormalization group theory. We find that disorder rounds the first-order quantum phase transition in agreement with quantum version of the Imry-Ma criterion --Abstract, page v

Contact process with temporal disorder

We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.Comment: 14 pages, 16 eps figures included. Final version as publishe

Phase Transitions on Random Lattices: How Random is Topological Disorder?

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of $\omega=(d-1)/(2d)$ in $d$ dimensions. %instead of the generic value $\omega=1/2$. The stability of clean critical points is thus governed by the criterion $(d+1)\nu > 2$ rather than the usual Harris criterion $d\nu>2$, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions $d>1$. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices.Comment: 4.5 pages, 4 eps figures, final version as publishe

Random Field Disorder at an Absorbing State Transition in One and Two Dimensions

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such random-field disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems