Properties of size-dependent models having quasiperiodic boundary conditions

Boundary conditions effects are explored for size-dependent models in thermal equilibrium. Scalar and fermionic models are used for $D=1+3$ (films), $D=1+2$ (hollow cylinder) and $D=1+1$ (ring). For all models a minimal length is found, below which no thermally-induced phase transition occurs. Using quasiperiodic boundary condition controlled by a contour parameter $\theta$ ($\theta=0$ is a periodic boundary condition and $\theta=1$ is an antiperiodic condition) it results that the minimal length depends directly on the value of $\theta$. It is also argued that this parameter can be associated to an Aharonov-Bohm phase.