# Non-markovian global persistence in phase-ordering kinetics

Source: [Non-markovian global persistence in phase-ordering kinetics](<https://www.sota2.com/research/paper/68fa28db1e209131ce82e9db>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:57.139Z

Authors: Malte Henkel, Michel Pleimling

Published: 2009-07-09T18:38:59.000Z

## Abstract

The persistence probability P\_g(t) of the global order-parameter of a simple ferromagnet undergoing phase-ordering kinetics after a quench from a fully disordered state to below the critical temperature, T\<T\_c, is analysed. It is argued that the persistence probability decays algebraically with time in the entire low-temperature phase. For Markov processes, the associated global persistence exponent theta\_g = (2 lambda\_C -d)/(2z) is related to the autocorrelation exponent lambda\_C. This relationship is confirmed for phase-ordering in the exactly solved 1D Ising model and the d-dimensional spherical model. For the 2D Glauber-Ising model, theta\_g=0.063(2) is found which indicates that the dynamics of the global order-parameter is described by a non-markovian process.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0907.1642>)

[PDF](<https://arxiv.org/pdf/0907.1642.pdf>)