Critical behaviour of a tumor growth model - Directed Percolation with a mean-field flavour

Abstract

We examine the critical behaviour of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report (Ferreira et al., Phys. Rev. E 85, 010901 (2012)), which suggested that the critical behaviour of the model differs from the expected Directed Percolation (DP) universality class. Surprisingly, only some of the critical exponents (beta, alpha, nu_perp, and z) take non-DP values while some others (beta', nu_||, and spreading-dynamics exponents Theta, delta, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations beta=alpha*nu_||, beta'=delta*nu_||, and the generalized hyperscaling relation Theta+alpha+delta=d/z, where the dynamical exponent z is, however, used instead of the spreading exponent z'. Both in d=1 and d=2 versions of our model, the exponent beta most likely takes the mean-field value beta=1, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient.