A Brief History of the Harris Criterion

In this talk I will briefly review the ``Harris criterion,'' which was given in a 1974 paper in J. Phys. C. This criterion indicates whether the critical exponents of a system at a phase transition are modified by the presence of locally random impurities. To frame the discussion and since the argument for the criterion is so simple, I will repeat its derivation here. Since some of those who quote the paper may not have actually read it in detail, I will discuss some of the applications given there to systems with randomness which have longer-range correlations and I will emphasize those aspects which are perhaps less well-known. Also, with the benefit of hindsight, I will slightly reinterpret some of the conclusions of the 1974 paper. To further put this work in context, I will discuss how the renormalization group indicated that this argument indeed captured the essential role of local randomneess. Later work on longer range models fits in nicely with the criterion. Finally, I will briefly mention experimental studies of this criterion. Perhaps the appropriate general conclusion from all of this is that a sound qualitative argument can have an honored place along side technically exact solutions.