Marginal relevance of disorder for pinning models

Details Marginal relevance of disorder for pinning models Marginal relevance of disorder for pinning models

2008-11-05

arxiv.org/abs/0811.0723v2

Commun. Pure Appl. Math. 63 Issue 2 (2010), 233-265

Physics

Mathematical Physics

27 pages. v2: section 4.1 simplified. To appear on Commun. Pure Appl. Math

Scientific paper

10.1002/cpa.20301

The effect of disorder on pinning and wetting models has attracted much attention in theoretical physics. In particular, it has been predicted on the basis of the Harris criterion that disorder is relevant (annealed and quenched model have different critical points and critical exponents) if the return probability exponent alpha, a positive number that characterizes the model, is larger than 1/2. Weak disorder has been predicted to be irrelevant (i.e. coinciding critical points and exponents) if alpha < 1/2. Recent mathematical work has put these predictions on firm grounds. In renormalization group terms, the case alpha = 1/2 is a 'marginal case' and there is no agreement in the literature as to whether one should expect disorder relevance or irrelevance at marginality. The question is particularly intriguing also because the case alpha = 1/2 includes the classical models of two-dimensional wetting of a rough substrate, of pinning of directed polymers on a defect line in dimension (3+1) or (1+1) and of pinning of an heteropolymer by a point potential in three-dimensional space. Here we prove disorder relevance both for the general alpha = 1/2 pinning model and for the hierarchical version of the model proposed by B. Derrida, V. Hakim and J. Vannimenus (JSP, 1992), in the sense that we prove a shift of the quenched critical point with respect to the annealed one. In both cases we work with Gaussian disorder and we show that the shift is at least of order exp(-1/\beta^4) for beta small, if beta is the standard deviation of the disorder.

Affiliated with

Also associated with

No associations

Rating

Marginal relevance of disorder for pinning models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Marginal relevance of disorder for pinning models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Marginal relevance of disorder for pinning models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-373550