Interaction dependence of the critical correlation length amplitude ratio in anisotropic scalar lattice $ϕ^4$ theory

We investigate critical correlations in the weakly anisotropic two-dimensional scalar lattice $ϕ^4$ theory and demonstrate that a previously reported independence of the correlation length amplitude ratio from the local interaction strength does not hold. Monte Carlo simulations instead reveal a pronounced dependence of this ratio on the interaction strength. As the coupling is increased, the amplitude ratio interpolates between the continuum and Ising limits, highlighting a nontrivial interplay between lattice effects and local interactions. These findings call for a revised theoretical description of anisotropy effects at finite coupling in this prototypical lattice field theory.