Interpolating the Sherrington–Kirkpatrick replica trick
نویسندگان
چکیده
منابع مشابه
Another Critique of the Replica Trick
Kamenev and Mezard, and Yurkevich and Lerner, have recently shown how to reproduce the large-frequency asymptotics of the energy level correlations for disordered electron systems, by doing perturbation theory around the saddles of the compact nonlinear σ model derived from fermionic replicas. We present a critical review of their procedure and argue that its validity is limited to the perturba...
متن کاملValidation of the Replica Trick for Simple Models
We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis consists of two analytical techniques, the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion), ...
متن کاملNonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions
In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of ...
متن کاملThe Kernel Trick for Distances
A method is described which, like the kernel trick in support vector machines (SVMs), lets us generalize distance-based algorithms to operate in feature spaces, usually nonlinearly related to the input space. This is done by identifying a class of kernels which can be represented as norm-based distances in Hilbert spaces. It turns out that common kernel algorithms, such as SVMs and kernel PCA, ...
متن کاملThe Birthday Trick with Lies
In this article, we determine the number of yes/no questions required to figure out a birthday (a number between 0 and 31) when up to r incorrect answers to these questions are allowed. In the language of error-correcting codes, we construct optimal (shortest possible length) codes of size 32 and minimal distance d for each positive integer d .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Philosophical Magazine
سال: 2012
ISSN: 1478-6435,1478-6443
DOI: 10.1080/14786435.2011.637979