Related papers: Replica symmetry breaking related to a general ult…
Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
Replica symmetry breaking solutions for the new replica anzats, related to general ultrametric spaces, are investigated. A variant of analysis on trees is developed and applied to the computation of the n\to0 limit in the new replica…
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…
The Replica Fourier Transform introduced previously is related to the standard definition of Fourier transforms over a group. Its use is illustrated by block-diagonalizing the eigenvalue equation of a four-replica Parisi matrix.
The consequences of replica-symmetry breaking on the structure of ultrametric matrices appearing in the theory of disordered systems is investigated with the help of representation theory, and the results are compared with those obtained by…
We consider $m$-th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered generalizations of the Fibonacci matrix. We introduce the…
Geometrical pictures for the family structure of fundamental particles are developed. They indicate that there might be a relation between the family repetition structure and the number of space dimensions.
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
Recently we have shown that the equivalence classes of metrics on the double of a metric space $X$ form an inverse semigroup. Here we define an inverse subsemigroup related to a family of isometric subspaces of $X$, which is more…
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
Results obtained by us are overviewed from a general set up. The universal $R$-matrix is exploited to obtain various important relations and structures involved in quantum group algebra, which are used subsequently for generating different…
In this paper we review the predictions of the replica approach on the probability distribution of the overlaps among replicas and on the sample to sample fluctuations of this probability. We stress the role of replica equivalence in…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…