Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model

Satya N. Majumdar (1) , Clément Sire (2)

1 AT&T Bell Laboratories
2 GPT-LPQ - Groupe de Physique Théorique (LPQ)

We study the decay of the probability for a non-Markovian stationary Gaussian walker not to cross the origin up to time $t$. This result is then used to evaluate the fraction of spins that do not flip up to time $t$ in the zero temperature Monte-Carlo spin flip dynamics of the Ising model. Our results are compared to extensive numerical simulations.

Mots clés: modèle d'Ising; exposant critique; transition de phase; Persistence; random processes; coarsening; spin system; phase separation; Ising model; critical exponent; phase transition; persistance; processus aléatoire; retour à l'équilibre; séparation de phase

Domaines: Adaptation et Systèmes auto-organisés [nlin.AO]; Dynamique Chaotique [nlin.CD]; Formation de Structures et Solitons [nlin.PS]; Autre [cond-mat.other]; Mécanique statistique [cond-mat.stat-mech]

Satya N. Majumdar, Clément Sire. Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model. Physical Review Letters, 1996, 77, pp.1420-1423. ⟨10.1103/PhysRevLett.77.1420⟩. ⟨hal-00004854⟩