  We study the scalar one-component two-dimensional (2D) $\phi^4$ model by
computer simulations, with local Metropolis moves. The equilibrium exponents of
this model are well-established, e.g. for the 2D $\phi^4$ model $\gamma= 1.75$
and $\nu= 1$. The model has also been conjectured to belong to the Ising
universality class. However, the value of the critical dynamical exponent $z_c$
is not settled. In this paper, we obtain $z_c$ for the 2D $\phi^4$ model using
two independent methods: (a) by calculating the relative terminal exponential
decay time $\tau$ for the correlation function $\langle \phi(t)\phi(0)\rangle$,
and thereafter fitting the data as $\tau \sim L^{z_c}$, where $L$ is the system
size, and (b) by measuring the anomalous diffusion exponent for the order
parameter, viz., the mean-square displacement (MSD) $\langle \Delta
\phi^2(t)\rangle\sim t^c$ as $c=\gamma/(\nu z_c)$, and from the numerically
obtained value $c\approx 0.80$, we calculate $z_c$. For different values of the
coupling constant $\lambda$, we report that $z_c=2.17\pm0.03$ and
$z_c=2.19\pm0.03$ for the two methods respectively. Our results indicate that
$z_c$ is independent of $\lambda$, and is likely identical to that for the 2D
Ising model. Additionally, we demonstrate that the Generalised Langevin
Equation (GLE) formulation with a memory kernel, identical to those applicable
for the Ising model and polymeric systems, consistently capture the observed
anomalous diffusion behavior.
