Properties of size-dependent models having quasiperiodic boundary conditions. (English) Zbl 1383.82016
Summary: 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.
MSC:
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
| 81T28 | Thermal quantum field theory |
| 35Q56 | Ginzburg-Landau equations |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 82B30 | Statistical thermodynamics |
Keywords:
quasiperiodic boundary conditions; finite-temperature field theory; finite-size effects; phase transition; Aharonov-Bohm effect; Casimir effectReferences:
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