Category: Statistics

Summary: Testing whether the critical moment ratio in 1+1D directed percolation is the same across lattice geometries and update rules.

Directed percolation is a canonical universality class for absorbing-state phase transitions, and many of its critical exponents are expected to depend only on dimension. This experiment asks whether a dimensionless steady-state moment ratio plays the same universal role across several microscopic realizations, including site, bond, and related contact-process variants.

Each trial simulates the process near criticality for multiple system sizes, estimates the steady-state density and its second moment, and forms the ratio R = <rho^2>/<rho>^2. By comparing that quantity across geometries and update rules, the experiment checks whether universality extends cleanly to this amplitude-like observable and not just to standard exponents.

That question has received less systematic numerical attention than exponent estimation. The value of the experiment is therefore comparative: it tests whether models in the same class really collapse onto the same critical ratio once finite-size and statistical errors are controlled.

Method: Repeated near-critical directed-percolation or contact-process simulations across system sizes, measuring steady-state density moments and comparing the dimensionless ratio across model variants.

What is measured: Moment ratio R, mean density, second density moment, system-size dependence, and agreement across update rules and lattice types.