  P\'{o}lya urn is a stochastic process in which balls are randomly drawn from
an urn of red and blue balls, and balls of the same color as the drawn balls
are added. The probability of a ball of a certain color being drawn is equal to
the percentage of balls of that color in the urn. We introduce arbitrary memory
kernels to modify this probability. If the memory kernel decays exponentially,
it is a stationary process and is mean-reverting. If the memory kernel decays
by a power-law, a phase transition occurs and the asymptotic behavior of the
autocorrelation function changes. An auxiliary field variable is introduced to
transform the process Markovian and the field obeys a multivariate
Ornstein-Uhlenbeck process. The exponents of the power law are estimated for
the decay of the leading and subleading terms of the autocorrelation function.
It is shown that the power law exponents changes discontinuously at the
critical point.
