Phase transitions and correlations in the bosonic pair contact process with diffusion: exact results

The variance of the local density of the pair contact process with diffusion is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for a lattice dimension d > 2 the variance exhibits a phase transition: for high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behaviour also appears in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z = 2