We examine the critical behavior 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(R) (2012)], which suggested that the critical behavior 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 (${\beta }^{\prime }$, ${\nu }_{\left|\right|}$, and spreading-dynamics exponents $\Theta$, $\delta$, $z^{\prime }$) remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations $\beta =\alpha {\nu }_{\left|\right|}$, ${\beta }^{\prime }=\delta {\nu }_{\left|\right|}$, and the generalized hyperscaling relation $\Theta +\alpha +\delta =d/z$, where the dynamical exponent $z$ is, however, used instead of the spreading exponent $z^{\prime }$. 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.

• Received 11 June 2012

DOI:https://doi.org/10.1103/PhysRevE.86.041138