Properties of size-dependent models having quasiperiodic boundary conditions

Boundary condition 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.