  Tricriticality, as a sister of criticality, is a fundamental and absorbing
issue in condensed matter physics. It has been verified that the bosonic
Wilson-Fisher universality class can be changed by gapless fermionic modes at
criticality. However, the counterpart phenomena at tricriticality have rarely
been explored. In this paper, we study a model in which a tricritical Ising
model is coupled to massless Dirac fermions. We find that the massless Dirac
fermions result in the emergence of a new tricritical point, which we refer to
as the chiral tricritical point (CTP), at the phase boundary between the Dirac
semimetal and the charge-density-wave insulator. From functional
renormalization group analysis of the effective action, we obtain the critical
behaviors of the CTP, which are qualitatively distinct from both the
tricritical Ising universality and the chiral Ising universality. We further
extend the calculations of the chiral tricritical behaviors of Ising spins to
the case of Heisenberg spins. The experimental relevance of the CTP in
two-dimensional Dirac semimetals is also discussed.
