Violations of Hyperscaling in Finite-Size Scaling above the Upper Critical Dimension

Abstract

We consider how finite-size scaling (FSS) is modified above the upper critical dimension, du=4, due to hyperscaling violations, which in turn arise from a dangerous irrelevant variable. In addition to the commonly studied case of periodic boundary conditions, we also consider new effects that arise with free boundary conditions. Some numerical results are presented in addition to theoretical arguments.

Keywords

• phase transitions
• finite-size scaling
• hyperscaling
• upper critical dimension