  We develop a systematic theory for the critical phenomena with memory in all
spatial dimensions, including $d<d_c$, $d=d_c$, and $d>d_c$, the upper critical
dimension. We show that the Hamiltonian plays a unique role in dynamics and the
dimensional constant $\mathfrak{d}_t$ that embodies the intimate relationship
between space and time is the fundamental ingredient of the theory. However,
its value varies with the space dimension continuously and vanishes exactly at
$d=4$, reflecting reasonably the variation of the amount of the temporal
dimension that is transferred to the spatial one with the strength of
fluctuations. Such variations of the temporal dimension save all scaling laws
though the fluctuation-dissipation theorem is violated. Various new
universality classes emerge.
