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

First order phase transition in the few-body XY-models with surface fields