Numerical study of the random field Ising model at zero and positive temperature

TL;DR

This study investigates the three-dimensional random field Ising model at zero and positive temperatures, analyzing critical behavior, ground states, and correlations, revealing sharp peaks in thermodynamic quantities and supporting the zero temperature fixed point hypothesis.

Contribution

It provides a comprehensive numerical analysis of the RFIM at both zero and positive temperatures, including critical exponents, ground state tilings, and correlations, using advanced algorithms and finite size scaling.

Findings

Critical exponent $eta$ near zero

Presence of sharp peaks in specific heat and susceptibility

Strong correlation between zero and positive temperature configurations

Abstract

In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the bond energy. The heat capacity exponent $\alpha$ is found to be near zero. The ground states are determined for a range of external field and disorder strength near the zero temperature critical point and the scaling of ground state tilings of the field-disorder plane is discussed. At positive temperature the specific heat and the susceptibility are obtained using the Wang-Landau algorithm. It is found that sharp peaks are present in these physical quantities for some realizations of systems sized $16^3$ and larger. These sharp peaks result from flipping large domains and correspond to large discontinuities in ground state bond energies. Finally, zero temperature and positive temperature spin configurations near the critical line are found to be highly correlated suggesting a strong version of the zero temperature fixed point hypothesis.