Boundary effects on finite-size scaling for the 5-dimensional Ising model

Abstract

High-dimensional ($d\ge 5$) Ising systems have mean-field critical exponents. However, at the critical temperature the finite-size scaling of the susceptibility $\chi$ depends on the boundary conditions. A system with periodic boundary conditions then has $\chi \propto L^{5/2}$. Deleting the $5L^4$ boundary edges we receive a system with free boundary conditions and now $\chi \propto L^2$. In the present work we find that deleting the $L^4$ boundary edges along just one direction is enough to have the scaling $\chi \propto L^2$. It also appears that deleting $L^3$ boundary edges results in an intermediate scaling, here estimated to $\chi \propto L^{2.275}$. We also study how the energy and magnetisation distributions change when deleting boundary edges.

7 pages, 16 figures

References in corpus (5)

• Finite-size scaling above the upper critical dimension
• Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
• Finite size scaling of the 5D Ising model with free boundary conditions
• The discontinuity of the specific heat for the 5D Ising model
• The effect of free boundary conditions on the Ising model in high dimensions

Cited by in corpus (4)

• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• The fifty-year quest for universality in percolation theory in high dimensions
• When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
• Phase transitions above the upper critical dimension