By Bikas K. Chakrabarti
With the mapping of the partition functionality graphs of the n-vector magnetic version within the n to zero restrict because the self-avoiding walks, the conformational facts of linear polymers was once in actual fact understood in early seventies. a number of types of disordered solids, percolation version specifically, have been additionally verified through past due seventies. as a consequence, investigations on thestatistics of linear polymers or of self-avoiding walks in, say, porous medium or disordered lattices have been begun in early eighties. regardless of the intense principles forwarded and wide reviews made for the following twenty years, the matter isn't but thoroughly solved in its generality. This exciting and significant challenge has remained when you consider that a subject of lively and lively research.This publication intends to provide the readers a primary hand and vast overview of a few of the facets of the matter, written through the specialists within the respective fields. we are hoping, the contents of the e-book will supply a invaluable consultant for researchers in statistical physics of polymers and should definitely result in additional examine and advances in the direction of a whole figuring out of the matter. · First e-book on information of polymers in random media.· Contents right away from learn labs.· Chapters written via most desirable specialists within the respective fields.· Theories, experiments and laptop simulations greatly discussed.· contains most modern advancements in realizing comparable very important subject matters like DNA unzipping, traveling salesman challenge, etc.· finished index for speedy look for keyword phrases.
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Extra info for Statistics of linear polymers in disordered media
Though written for a general potential V(r), we shall consider only short-range interaction that, when convenient, can be replaced by a 8-function. 1. Annealed case: two chain As expected, the average partition function (annealed averaging) would correspond to a pure-type problem. This however is not the case always as we see in Sec. 3 for more than two chains. A straightforward averaging of Z = J Dr 1 Dr 2 exp( -H) using the probability distribution of Eq. etr), and it is given by 1letr = ~ 1N dz t (iJr~;z)) 2 + Vo 1N dz V(r12(z))- v526.
This exponent is independent of temperature but depends on b. As mentioned, in the site version there are special sites with large degree. Whether such vertices lead to a Griffiths' type singularity needs to explored. Griffiths singularity in the context of random interactions has recently been discussed in Ref. . 2. Bond randomness: Problem with Harris criterion 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 directed polymer problem .
G. for low dimensions, at u* = 0, the effect of the disorder can be obtained from the RG flow of r 0 • Defining the dimensionless coupling constant r0 = r0 L 2'' where E1 = 1- d with r(L) as the dimensionless running coupling constant, the RG equation is given by [36,37] dr 2 LdL =2(b+r ). (74) There are two fixed points (i) r = 0, and (ii) r* = -E1. , ford> 1. See Appendix H for details. S. M. Bhattacharjee 36 We see certain similarities of disorder or randomness becoming marginally relevant at some dimension: de = 2 for the random medium problem, but de = 1 for the RANI problem.