Harris criterion

We will discuss if the size exponents (i/ or ve) are affected by the lattice (configurational) fluctuations if r (p) is different from i/ or if i/ is different from i/J for p < 1. This question arises naturally from the application of the Harris criterion [8] to the n-vector model in the n —> 0 limit [2], when the partition function graphs are all SAWs. A naive application of the criterion to the SAWs suggested [6] a possible disorder induced crossover in the critical behaviour of SAW statistics for any amount of disorder (p < 1). A modified... 

The problem of a polymer in a random medium was initiated by Chakrabarti and Kertesz [4,5] with the application of the Harris criterion. This problem has enriched our overall understanding of polymers and random systems in general, but still a complete understanding remains elusive. Not surprisingly, the look out for simpler problems that capture the basic essence of the original complex system gained momentum. In this context, directed polymers played a very crucial role. 

According to the Harris criterion, disorder is irrelevant at a critical point if the pure specific heat exponent a < 0. We show that a more general criterion is required for the... 

In order to construct a general framework for checking the validity of the Harris criterion, we start with the Taylor expansion of the recursion relation of Eq. (86),... 

Hence, the Harris criterion holds good if either... 

If the disordered models are classified by according to the sign of a, and I or R according to irrelevance or relevance of disorder, then the Harris criterion suggests the existence of only two classes (+R) and (-1). On the other hand, the above inequalities allow special classes like (-I-I) and (-R) where the Harris criterion fails. Model A is in the (-I-I) class for 6 > 2 - - - /2. Model B is in either the (-I-R) or (-1) class depending on 6. It is possible to construct models that would belong to any of the four possible classes, especially (-R) [46]. 

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. 

For magnetic systems, the effect of weak quenched uncorrelated point-like disorder on the critical behavior is usually predicted by the Harris criterion [40] disorder changes the critical exponents only if the specific heat critical exponent ap re of the pure (undiluted) system is positive ... 

The straightforward application of the Harris criterion to the statics of SAWs indicates, that the critical exponents should be modified in the presence of any amount of lattice... 

What is One Expecting The Renormalization Gronp Viewpoint and the Harris Criterion... 

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