  We investigate the one-dimensional finite-size XY model with opposing surface
fields in the X direction. Exact solutions are obtained for the two-site and
three-site models, while numerical methods are employed for models with more
than three sites. Remarkably, first-order quantum phase transitions are
observed in this system. At the phase transition point, the energy gap closes
linearly, and the magnetization at each site undergoes a discontinuous jump.
Additionally, we identify a $Z_2$ symmetry that accompanies the phase
transition and its associated symmetry change. Notably, the first-order phase
transition in finite-size systems does not exhibit the conventional finite-size
rounding effect. On the contrary, there exists a counterintuitive finite-size
effect: the amplitude of the jump in magnetization at each site decreases as
the lattice size increases. Interestingly, lattices with an even number of
sites share a common phase boundary, while lattices with an odd number of sites
have a distinct phase boundary.
