  We propose a tensor-network algorithm for discrete-time stochastic dynamics
of a homogeneous system in the thermodynamic limit. We map a $d$-dimensional
nonequilibrium Markov process to a $(d+1)$-dimensional infinite tensor network
by using a higher-order singular-value decomposition. As an application of the
algorithm, we compute the nonequilibrium relaxation from a fully magnetized
state to equilibrium of the one- and two- dimensional Ising models with
periodic boundary conditions. Utilizing the translational invariance of the
systems, we analyze the behavior in the thermodynamic limit directly. We
estimated the dynamical critical exponent $z=2.16(5)$ for the two-dimensional
Ising model. Our approach fits well with the framework of the
nonequilibrium-relaxation method. Our algorithm can compute time evolution of
the magnetization of a large system precisely for a relatively short period. In
the nonequilibrium-relaxation method, on the other hand, one needs to simulate
dynamics of a large system for a short time. The combination of the two
provides a new approach to the study of critical phenomena.
