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

TL;DR

This paper analyzes the survival probability of a Gaussian non-Markovian process and applies the findings to understand spin dynamics in the zero-temperature Ising model, supported by numerical simulations.

Contribution

It provides a novel analytical approach to the decay of survival probability in non-Markovian Gaussian processes and applies it to spin dynamics in the Ising model.

Findings

Derived decay laws for survival probability

Quantitative agreement with numerical simulations

Insights into zero-temperature spin flip dynamics

Abstract

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.