The scaling window of the 5D Ising model with free boundary conditions

TL;DR

This paper investigates the finite-size scaling of the susceptibility in the 5D Ising model with free boundary conditions, providing evidence supporting the conventional $O(L^2)$ scaling within a $O(1/L^2)$ window near criticality.

Contribution

It offers comprehensive Monte Carlo analysis confirming the standard finite-size scaling behavior of susceptibility and cluster properties in the 5D Ising model with free boundaries.

Findings

Susceptibility scales as $O(L^2)$ within a $O(1/L^2)$ window.

Cluster behavior aligns with mean field critical exponent $eta=1/3$.

Results support the conventional finite-size scaling picture.

Abstract

The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the conventional scaling picture, where the susceptibility scales as $O(L^2)$ inside a critical scaling window of width $O(1/L^2)$. Our results are based on Monte Carlo data gathered on system sizes up to $L=79$ (ca. three billion spins) for a wide range of temperatures near the critical point. We analyse the magnetisation distribution, the susceptibility and also the scaling and distribution of the size of the Fortuin-Kasteleyn cluster containing the origin. The probability of this cluster reaching the boundary determines the correlation length, and its behaviour agrees with the mean field critical exponent $\delta=3$, that the scaling window has width $O(1/L^2)$.