Surface criticality in random field magnets

TL;DR

This paper investigates the surface critical behavior of three-dimensional random field Ising magnets near the critical point using combinatorial optimization, revealing how boundary disorder affects surface and bulk scaling laws.

Contribution

It provides the first detailed analysis of surface critical exponents in random field magnets, showing how boundary disorder influences surface and bulk phase transition relations.

Findings

Surface magnetization exponent $eta_1$ measured.

Surface excess exponents $eta_s$ and $\alpha_s$ determined.

Boundary disorders decay faster than bulk disorder.

Abstract

The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: $\beta_1$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, $\beta_s$ and $\alpha_s$. The latter ones are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of hyperscaling exponent $\theta$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.