Ground state numerical study of the three-dimensional random field Ising model

TL;DR

This study investigates the critical behavior of the three-dimensional random field Ising model at zero temperature, revealing near-zero critical exponents through numerical analysis of ground states.

Contribution

It provides a detailed numerical analysis of the ground states of the 3D RFIM, identifying critical points and exponents with finite-size scaling methods.

Findings

Critical exponents near zero for magnetization and specific heat

Identification of finite-size critical points via ground state degeneracies

Ground state discontinuities used to determine phase transition characteristics

Abstract

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.