The three-dimensional random-field Ising model is studied by Monte Carlo simulations on $L\times L\times L$ lattices with $L<~64$. Our results are completely consistent with there being a ferromagnetically ordered state at low temperatures. For $T\to T_c^{+}$, the susceptibility and correlation length have effective exponents similar to the pure two-dimensional Ising model. However, for the random-field values studied, the transition is actually first order, driven by large fluctuations in the disconnected correlation functions. We suggest that the transition is first order, even for arbitrarily small values of the random field.

• Received 19 March 1985

DOI:https://doi.org/10.1103/PhysRevLett.54.2429