  The well-established universality classes of absorbing critical phenomena are
directed percolation (DP) and directed Ising (DI) classes. Recently, the pair
contact process with diffusion (PCPD) has been investigated extensively and
claimed to exhibit a new type of critical phenomena distinct from both DP and
DI classes. Noticing that the PCPD possesses a long-term memory effect, we
introduce a generalized version of the PCPD (GPCPD) with a parameter
controlling the memory effect. The GPCPD connects the DP fixed point to the
PCPD point continuously. Monte Carlo simulations show that the GPCPD displays
novel type critical phenomena which are characterized by continuously varying
critical exponents. The same critical behaviors are also observed in models
where two species of particles are coupled cyclically. We suggest that the
long-term memory may serve as a marginal perturbation to the ordinary DP fixed
point.
