J un 1 99 9 P - adic numbers and replica symmetry breaking February 1 , 2008
نویسنده
چکیده
The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic Fourier transform seems to be an promising tool. Unité Propre du Centre National de la Recherche Scientifique, associée à l’ Ecole Normale Supérieure et à l’Université de Paris-Sud.
منابع مشابه
J un 1 99 5 Unrealizable Learning in Binary Feed - Forward Neural Networks DRAFT February 1 , 2008
Statistical mechanics is used to study unrealizable generalization in two large feed-forward neural networks with binary weights and output, a perceptron and a tree committee machine. The student is trained by a teacher being larger, i.e. having more units than the student. It is shown that this is the same as using training data corrupted by Gaussian noise. Each machine is considered in the hi...
متن کاملar X iv : c on d - m at / 9 40 50 07 v 1 4 M ay 1 99 4 Interfaces and lower critical dimension in a spin glass model
In this paper we try to estimate the lower critical dimension for replica symmetry breaking in spin glasses through the calculation of the additional free-energy required to create a domain wall between two different phases. This mechanism alone would say that replica symmetry would be restored at the lower critical dimension D c = 2.5.
متن کامل2 N ov 1 99 9 How to break the replica symmetry in structural glasses
The variational principle (VP) has been used to capture the metastable states of a glass-forming molecular system without quenched disorder. It has been shown that VP naturally leads to a self-consistent random field Ginzburg-Landau model (RFGLM). In the framework of one-step replica symmetry breaking (1-RSB) the general solution of RFGLM is discussed in the vicinity of the spinodal temperature...
متن کاملar X iv : 0 80 6 . 08 36 v 1 [ m at h . A G ] 4 J un 2 00 8 p - ADIC HURWITZ NUMBERS
We introduce stable tropical curves, and use these to count covers of the p-adic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers.
متن کاملA ug 1 99 8 Replica analysis of the p - spin interactions Ising spin - glass model
The thermodynamics of the infinite-range Ising spin glass with p-spin interactions in the presence of an external magnetic field h is investigated analytically using the replica method. We give emphasis to the analysis of the transition between the replica symmetric and the one-step replica symmetry breaking regimes. In particular, we derive analytical conditions for the onset of the continuous...
متن کامل