The ising model in a random magnetic field.
01 January 1984
The existence of a spontaneous magnetization in the three dimensional Ising Model in a weak random field (RFIM) is investigated. Under the unproven assumption that the expectation value of the spin at one site is weakly correlated with the random field at far away sites (which is true if surfaces within surfaces can be ignored) it follows that the three dimensional RFIM has a spontaneous magnetization at low temperatures.