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Probability distribution of persistent spins in an Ising chain

P. K. Das,P. Sen

Published 2004 in Journal of Physics A

ABSTRACT

We study the probability distribution Q(n, t) of n(t), the fraction of spins unflipped up to time t, in an Ising chain with ferromagnetic interactions. The distribution shows a peak at n = nmax and in general is non-Gaussian and asymmetric in nature. However, for n > nmax it shows a Gaussian decay. Data collapse can be obtained when Q(n, t)/Lα versus (n − nmax)Lβ is plotted with α ~ 0.45 and β ~ 0.6. Interestingly, nmax(t) shows different behaviour compared to n(t) = P(t), the persistence probability which follows the well-known behaviour P(t) ~ t−θ. A quantitative estimate of the asymmetry and non-Gaussian nature of Q(n, t) is made by calculating its skewness and kurtosis.

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