Probability distribution of persistent spins in a Ising chain

We study the probability distribution $Q(n,t)$ of $n(t)$, the fraction of spins unflipped till time $t$, in a Ising chain with ferromagnetic interactions. The distribution shows a peak at $n=n_{max}$ and in general is non-Gaussian and asymmetric in nature. However for $n>n_{max}$ it shows a Gaussian decay. A data collapse can be obtained when $Q(n,t)/L^{\alpha}$ versus $(n-n_{max})L^{\beta}$ is plotted with $\alpha \sim 0.45$ and $\beta \sim 0.6$. Interestingly, $n_{max}(t)$ shows a different behaviour compared to $<n(t)> = P(t)$, the persistence probability which follows the well-known behaviour $P(t)\sim t^{-\theta}$. A quantitative estimate of the asymmetry and non-Gaussian nature of $Q(n,t)$ is made by calculating its skewness and kurtosis.