  The fluctuations of massless Dirac fermion can not only turn a first-order
bosonic phase transition (in the Landau sense) to a quantum critical point, but
also work reversely to enhance the first-order transition itself, depending on
the implementation of finite size effects in the coupling corrections. Here, we
report a case study of the latter by employing quantum Monte Carlo simulation
upon a lattice model in which the bosonic part featuring the Landau-Devonshire
first-order phase transition and Yukawa coupled to the Dirac fermions. We find
that the parameter range for the first-order phase transition becomes larger as
the Yukawa coupling increases and the microscopic mechanism of this phenomena
is revealed, at a quantitative level, as the interplay between the critical
fluctuations and the finite-size effects. Moreover, the scaling behavior at the
separation point between the first-order and the continuous phase transitions
is found to belong to the chiral tricritical Gross-Neveu universality. Our
result demonstrates that the interplay of massless Dirac fermions, critical
fluctuations and the finite size effects could trigger a plethora of
interesting phenomena and therefore great care is called for when making
generalizations.
