Excitations in high-dimensional random-field Ising magnets

TL;DR

This paper investigates excitations in high-dimensional random-field Ising magnets using large-scale numerical ground-state calculations, revealing how properties like stiffness and fractal dimensions behave across dimensions up to the upper critical dimension.

Contribution

It provides the first comprehensive numerical analysis of excitations in high-dimensional RFIMs, confirming scaling relations and elucidating dimension-dependent properties.

Findings

Scaling relations are fulfilled below the upper critical dimension.

Stiffness exponents can be derived from ground-state energy scaling for d<6.

Large system sizes of over five million spins were analyzed.

Abstract

Domain walls and droplet-like excitation of the random-field Ising magnet are studied in d={3,4,5,6,7} dimensions by means of exact numerical ground-state calculations. They are obtained using the established mapping to the graph-theoretical maximum-flow problem. This allows to study large system sizes of more than five million spins in exact thermal equilibrium. All simulations are carried out at the critical point for the strength h of the random fields, h=h_c(d), respectively. Using finite-size scaling, energetic and geometric properties like stiffness exponents and fractal dimensions are calculated. Using these results, we test (hyper) scaling relations, which seem to be fulfilled below the upper critical dimension d_u=6. Also, for d<d_u, the stiffness exponent can be obtained from the scaling of the ground-state energy.