Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models

TL;DR

This study investigates how boundary conditions influence phase transition behaviors in high-dimensional Ising models, revealing boundary effects and quasi-first order transitions in dimensions 4 and 5, with implications for understanding critical phenomena.

Contribution

It provides a comparative analysis of boundary effects on specific heat and entropy derivatives in high-dimensional Ising models, highlighting boundary-induced quasi-first order transitions in 4D and 5D.

Findings

Boundary strongly affects critical behavior in 4D and 5D.

Cyclic boundaries in 5D exhibit bimodal energy distributions.

Latent heat diminishes with system size but remains observable.

Abstract

In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -dS/dU. In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi first order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.