Marginal relevance disorder

We see certain similarities of disorder or randomness becoming marginally relevant at some dimension dc = 2 for the random medium problem, but dc = l for the RANI problem. A new fixed point emerges above this critical dimension. For the random medium problem, this implies the existence of a new phase and a disorder induced phase transition, but for the random interaction problem it defines a new type of critical behaviour. These results based on the exact RG analysis [36,37] were later on also recovered from a dynamic renormalization group study [38]. 

The RANI model remains less understood compared to the random medium problem. Exact renormalization analysis establish the marginal relevance of the disorder at d = 1, indicating a disorder dominated unbinding transition in d > 1. Several features including a generalization of the Harris criterion for this criticality via relevant disorder and aspects of unzipping have been discussed. 

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