  Rumor and information spreading are natural processes that emerge from
human-to-human interaction. Mathematically, this was explored in the popular
Maki-Thompson model, where a phase transition was thought to be absent. Here,
we show that a second-order phase transition is present in this model which is
not captured by first-order mean-field approximations. Moreover, we propose and
explore a modified version of the Maki-Thompson model that includes a
forgetting mechanism. This modification changes the Markov chain's nature from
infinitely many absorbing states in the classical setup to a single absorbing
state. In practice, this allows us to use a plethora of analytic and numeric
methods that permit the models' characterization. In particular, we find a
counter-intuitive behavior in the subcritical regime of these models, where the
lifespan of a rumor increases as the spreading rate drops, following a
power-law relationship. This means that, even below the critical threshold,
rumors can survive for a long time. Together, our findings suggest that the
dynamic behavior of rumor models can be much richer than previously thought.
Thus, we hope that our results motivate further research both analytically and
numerically.
