Direct measurement of correlation length in one-dimensional contact process

We investigate the contact process in one dimension by a quantity K ( L , t ) to measure the spatial correlation length. K(L,t) = Lσ ^2 / ⟨ρ⟩ ^2 is defined as a function of time, where L , ρ , σ ^2 , and ⟨⋯⟩ are the system size, the particle density, the variance of ρ , and the ensemble average, respectively. At the critical point, K ( t ) follows a power law of K(t) ∼ t^1/z with z=1.5821(16) . We estimate the correlation length exponent ν _⊥ = 1.1014(33) using the relation K_stat(p) ∼ (p_c - p)^-ν _⊥ in the subcritical regime, where K_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 ).