Direct measurement of correlation length in one-dimensional contact process

Abstract

We investigate the contact process in one dimension by a quantity K(L, t) to measure the spatial correlation length. $K(L,t) = L\sigma ^2 / \langle \rho \rangle ^2$ is defined as a function of time, where L, $\rho$, $\sigma ^2$, and $\langle \cdots \rangle$ are the system size, the particle density, the variance of $\rho$, and the ensemble average, respectively. At the critical point, K(t) follows a power law of $K(t) \sim t^{1/z}$ with $z=1.5821(16)$. We estimate the correlation length exponent $\nu _\perp = 1.1014(33)$ using the relation $K_\mathrm {stat}(p) \sim (p_c - p)^{-\nu _\perp }$ in the subcritical regime, where $K_\mathrm {stat}$ is the stationary value of K. K(t) is proportional to the correlation length therefore we could obtain the information of the correlation length directly using K(t).