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

Abstract

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.

arXiv comment11 pages, 8 eps figures included

References in corpus (21)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Method for Generating Long-Range Correlations for Large Systems
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Recurrence time analysis, long-term correlations, and extreme events
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Strong disorder fixed point in absorbing state phase transitions
• Disorder-induced rounding of certain quantum phase transitions
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Absorbing state phase transitions with quenched disorder
• Quantum Griffiths effects in itinerant Heisenberg magnets
• Critical behavior and Griffiths effects in the disordered contact process
• Criticality and quenched disorder: rare regions vs. Harris criterion
• Smearing of the phase transition in Ising systems with planar defects
• Reweighting in nonequilibrium simulations
• Monte-Carlo simulations of the clean and disordered contact process in three dimensions
• Disorder promotes ferromagnetism: Rounding of the quantum phase transition in Sr_{1-x}Ca_xRuO_3
• Broadening of a nonequilibrium phase transition by extended structural defects
• Random quantum magnets with long-range correlated disorder: Enhancement of critical and Griffiths-McCoy singularities
• Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process
• Disorder correlations at smeared phase transitions

Cited by in corpus (11)

• Disorder in quantum many-body systems
• Strong Disorder RG approach - a short review of recent developments
• Fractional Brownian motion with a reflecting wall
• Reflected fractional Brownian motion in one and higher dimensions
• The correlation functions of certain random antiferromagnetic spin-1/2 critical chains
• Extinction transitions in correlated external noise
• Extinction phase transitions in a model of ecological and evolutionary dynamics
• Non-Gaussian behavior of reflected fractional Brownian motion
• Random field disorder at an absorbing state transition in one and two dimensions
• Critical properties of the Susceptible-Exposed-Infected model with correlated temporal disorder
• Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model