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In this paper the three dimensional random field Ising model is studied atboth zero temperature and positive temperature. Critical exponents areextracted at zero temperature by finite size scaling analysis of largediscontinuities in the bond energy. The heat capacity exponent $\alpha$ isfound to be near zero. The ground states are determined for a range of externalfield and disorder strength near the zero temperature critical point and thescaling of ground state tilings of the field-disorder plane is discussed. Atpositive temperature the specific heat and the susceptibility are obtainedusing the Wang-Landau algorithm. It is found that sharp peaks are present inthese physical quantities for some realizations of systems sized $16^3$ andlarger. These sharp peaks result from flipping large domains and correspond tolarge discontinuities in ground state bond energies. Finally, zero temperatureand positive temperature spin configurations near the critical line are foundto be highly correlated suggesting a strong version of the zero temperaturefixed point hypothesis.Comment: 11 pages, 14 figure

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