Two-dimensional Super-roughening in Three-dimensional Ising Model

TL;DR

This paper introduces a geometric spin cluster representation of the 3D Ising model, revealing super-roughening and anomalous scaling at the critical temperature through extensive simulations.

Contribution

It presents a novel geometric interface approach to analyze the 3D Ising model and uncovers super-roughening phenomena with associated scaling behavior.

Findings

Criticality indicated by a size-independent cusp in interfacial width.

Emergence of super-roughening at the 2D cross section.

Geometric exponents match those of the 2D Ising model.

Abstract

We present a random-interface representation of the three-dimensional (3D) Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model and its 2D cross section. Extensive simulations have been carried out to measure the global interfacial width as a function of temperature for different lattice sizes which is shown to signal the criticality of the model at $T_c$ by forming a size-independent cusp in 3D, along with an emergent super-roughening at its 2D cross section. We find that the super-rough state is accompanied by an intrinsic anomalous scaling behavior in the local properties characterized by a set of geometric exponents which are the same as those for a pure 2D Ising model.