  Physics of quantum critical point is one of the most perplexing topics in
current condensed-matter physics. Its conclusive understanding is forestalled
by the scarcity of experimental systems displaying novel aspects of quantum
criticality. We present a comprehensive experimental evidence of a magnetic
field tuned tricritical point separating paramagnetic, antiferromagnetic and
metamagnetic phases in novel compound CePtIn$_4$. Analyzing field variations of
its magnetic susceptibility, magnetoresistance and specific heat at very low
temperatures, we trace modifications of antiferromagnetic structure of the
compound. Upon applying magnetic field of increasing strength, the system
undergoes metamagnetic transitions which persist down to the lowest temperature
investigated, exhibiting first-order-like boundaries separating magnetic
phases. This yields a unique phase diagram where the second-order phase
transition line terminates at a tricritical point followed by two first-order
lines reaching quantum critical end points as $T\to$~0. Our findings
demonstrate that CePtIn$_4$ provides innovative perspective for studies of
quantum criticality.
