Properties of size-dependent models having quasiperiodic boundary conditions

TL;DR

This study investigates how quasiperiodic boundary conditions influence minimal length thresholds for phase transitions in size-dependent thermal models across various geometries, linking boundary phase parameters to Aharonov-Bohm effects.

Contribution

It introduces the impact of quasiperiodic boundary conditions on minimal length and phase transitions in size-dependent models, connecting boundary phase parameters to Aharonov-Bohm phases.

Findings

Minimal length exists below which no phase transition occurs.

Quasiperiodic boundary conditions affect the minimal length.

Boundary phase parameter relates to Aharonov-Bohm phase.

Abstract

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.