Global Persistence Exponent for Critical Dynamics

Abstract

A `persistence exponent' $\theta$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t)\sim t^{-\theta }$, that the global order parameter has not changed sign in the time interval $t$ following a quench to the critical point from a disordered state. This exponent is calculated in mean-field theory, in the $n=\infty$ limit of the $O(n)$ model, to first order in $\epsilon =4-d$, and for the 1-d Ising model. Numerical results are obtained for the 2-d Ising model. We argue that $\theta$ is a new independent exponent.

4 pages, revtex, one figure

References in corpus (3)

• Nontrivial Exponent for Simple Diffusion
• Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes
• Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model

Cited by in corpus (117)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Universal scaling behavior of non-equilibrium phase transitions
• Generalized Dynamic Scaling for Critical Magnetic Systems
• Random Walks in Logarithmic and Power-Law Potentials, Nonuniversal Persistence, and Vortex Dynamics in the Two-Dimensional XY Model
• Experimental Measurement of the Persistence Exponent of the Planar Ising Model
• Large deviations and nontrivial exponents in coarsening systems
• Persistence in Complex Systems
• Deterministic Equations of Motion and Dynamic Critical Phenomena
• Persistence with Partial Survival
• Domain Statistics in Coarsening Systems
• Temporal and spatial persistence of combustion fronts
• Non-Markovian Persistence and Nonequilibrium Critical Dynamics
• Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models
• Residence Time Distribution for a Class of Gaussian Markov Processes
• Measurement of persistence in 1D diffusion
• Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries
• The longest excursion of stochastic processes in nonequilibrium systems
• Anomalous diffusion in disordered media and random quantum spin chains
• On universality in aging ferromagnets
• Dynamic Simulations of the Kosterlitz-Thouless Phase Transition
• Persistence in higher dimensions : a finite size scaling study
• Short time dynamics of a two dimensional majority vote model
• Monte Carlo Measurement of the Global Persistence Exponent
• Numerical study of persistence in systems with absorbing states
• Competition between Two Kinds of Correlations in Literary Texts
• Ageing in the critical contact process: a Monte Carlo study
• Stationary definition of persistence for finite temperature phase ordering
• Persistence, Poisoning, and Autocorrelations in Dilute Coarsening
• Persistence Probabilities of the German DAX and Shanghai Index
• Analytical results for random walk persistence
• Persistence of Manifolds in Nonequilibrium Critical Dynamics
• Domain Number Distribution in the Nonequilibrium Ising Model
• Global Persistence in Directed Percolation
• Persistence and dynamics in ANNNI chain
• Local Persistence in the Directed Percolation Universality Class
• Persistence in a Stationary Time-series
• Global persistence exponent of the two-dimensional Blume-Capel model
• Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance
• Relevant Stylized Facts About Bitcoin: Fluctuations, First Return Probability, and Natural Phenomena
• A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates
• Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models
• Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions
• Spherical model of growing interfaces
• Kinetics of Fluid Phase Separation
• Zero Temperature Dynamics of the Weakly Disordered Ising Model
• Statistics of occupation time and connection to local properties of non-homogeneous random walks
• Persistence in the two dimensional ferromagnetic Ising model
• On logarithmic extensions of local scale-invariance
• Dynamic SU(2) Lattice Gauge Theory at Finite Temperature
• Statistics of the occupation time for a class of Gaussian Markov processes
• Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks
• Probability distribution of the maximum of a smooth temporal signal
• An alternative order parameter for the 4-state Potts model
• Nonequilibrium critical dynamics in inhomogeneous systems
• Monte Carlo Simulations of Short-time Critical Dynamics with a Conserved Quantity
• Crossing intervals of non-Markovian Gaussian processes
• Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
• Dynamic crossover in the global persistence at criticality
• Average persistence in random walks
• Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model
• Short-time dynamics of polypeptides
• Persistence and Quiescence of Seismicity on Fault Systems
• Time-dependent Monte Carlo simulations of the critical and Lifshitz points of the ANNNI model
• Persistence in an antiferromagnetic Ising model with conserved magnetisation
• Memory functions and Correlations in Additive Binary Markov Chains
• Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation
• Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model
• Non-equilibrium critical dynamics in disordered ferromagnets
• Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics
• On the emergence of memory in equilibrium versus non-equilibrium systems
• Persistence and survival in equilibrium step fluctuations
• Fraction of uninfected walkers in the one-dimensional Potts model
• Finite Size Effect in Persistence
• Persistence of a Brownian particle in a Time Dependent Potential
• Persistence in Brownian motion of an ellipsoidal particle in two dimensions
• Global persistence exponent of the double-exchange model
• Kinetics of Ferromagnetic Ordering in 3D Ising Model: Do we understand the case of zero temperature quench?
• Non-equilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line
• Non Markovian persistence in the diluted Ising model at criticality
• Record Ages of Scale Invariant non-Markovian Random Walks
• Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover
• Persistence exponents of non-Gaussian processes in statistical mechanics
• Time correlations and persistence probability of a Brownian particle in a shear flow
• Analytical results for generalized persistence properties of smooth processes
• Stocks and Cryptocurrencies: Anti-fragile or Robust?
• Nonuniversality in short-time critical dynamics
• Persistence in Advection of Passive Scalar
• Persistence of an active asymmetric rigid Brownian particle in two dimensions
• Early-time critical dynamics of lattices of coupled chaotic maps
• Non-markovian global persistence in phase-ordering kinetics
• A comparative study of the dynamic critical behavior of the four-state Potts like models
• Persistence in the zero-temperature dynamics of the $Q$-states Potts model on undirected-directed Barabási-Albert networks and Erdös-Rényi random graphs
• Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model
• Short-time dynamics in the 1D long-range Potts model
• Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
• Microscopic Deterministic Dynamics and Persistence Exponent
• Correlation properties of the random linear high-order Markov chains
• Machine learning stochastic differential equations for the evolution of order parameters of classical many-body systems in and out of equilibrium
• Persistence exponents in a 3D symmetric binary fluid mixture
• Persistence Exponents and Scaling In Two Dimensional XY model and A Nematic Model
• Isotropy Properties of the Multi-Step Markov Symbolic Sequences
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Correlators in phase-ordering from Schrödinger-invariance
• Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes
• Diffusive Persistence on Disordered Lattices and Random Networks
• Dynamic crossover in the persistence probability of manifolds at criticality
• Finite-size effects in dynamics of zero-range processes
• Spatial patterns of random walkers under evolution of the attractiveness: persistent nodes, degree distribution, and spectral properties
• Local and global persistence exponents of two quenched continuous lattice spin models
• Probability distribution of persistent spins in a Ising chain
• Emergence of dynamic phases in the presence of different kinds of open boundaries in stochastic transport with short-range interactions
• Persistence of Non-Markovian Gaussian Stationary Processes in Discrete Time
• Dynamical critical behavior on the Nishimori point of frustrated Ising models
• Fluctuations and Persistence in Quantum Diffusion on Regular Lattices
• A statistical physics perspective on alignment-independent protein sequence comparison