Parallel plates and critical exponents for periodic and antiperiodic boundary conditions

We introduce a renormalized 1PI vertex part scalar field theory setting in momentum space to computing the critical exponents nu and eta,at least at two-loop order, for a layered parallel plate geometry separated by a distance L, with periodic as well as antiperiodic boundary conditions on the plates. We utilize massive as well as massless fields in order to extract the exponents in independent ultraviolet and infrared scaling analysis, respectively, which are required in a complete description of the scaling regions for finite size systems. Avoiding the crossover regimes, the three regions of finite size scaling present for each of these boundary conditions are shown to be indistinguishable in the results of the exponents in periodic and antiperiodic conditions, which coincide with those from,the (bulk) infinite system.