Condensed Matter

Zeta-Pad'e SRWS Theory with Approximation of Averaged Summation

Authors: Yoshiki Ueoka
Comments: 7 Pages. High dimensional approximation used in previous version becomes not necessary.

In my previous paper about Statistical Random Walk Summation(SRWS) theory[1], I proposed a new expansion of typical critical Green function for the Anderson transition in the Orthogonal class. In this paper, I perform an approximate summation for the series of the typical critical Green function. Pad'e approximant is used to take a summation. The new approximate expression of the critical exponent nu of localization length is obtained. The dimensional dependence of the critical exponent is directly related with Riemann zeta function. Thus, the number theory and the critical phenomena of the Anderson transition is connected. Therefore I call this method as zeta-Pad'e SRWS theory. Existence of lower critical dimension is understood as the infinite existence of prime numbers. Besides it, analogy with statistical mechanics also becomes clear.
Category: Condensed Matter

Along the Side of the Onsager's Solution, the Ekagi Language-Part Three

Authors: Anindya Kumar Biswas
Comments: 9 Pages.

We continue to consult the Ekagi-Dutch-English-Indonesian Dictionary by J. Steltenpool. In this short note, we remove all the multiple countings of an entry in a letter's section which have gone in in the companion paper "Along the side of the Onsager's solution, the Ekagi language; viXra: 2205.0065[Condensed Matter]". We draw the natural logarithm of the number of entries, denoted as f, normalised, starting with a letter vs the natural logarithm of the rank of the letter, denoted as k. We find that $\frac{lnf}{lnf_{max}}$ vs $\frac{lnk}{lnk_{lim}}$ is matched by the graph of the reduced magnetisation vs the reduced temperature of the exact Onsager solution of the two dimensional Ising model in the absence of the external magnetic field
Category: Condensed Matter

A Method for Studying the Anderson Transition in the Orthogonal Symmetry Class Employing a Random Walk Expansion, the Statistics of Asymptotic Walks and Summation Method

Authors: Yoshiki Ueoka
Comments: 17 Pages. High dimensional approximation used in previous version becomes not necessary.

I propose a method to study the Anderson transition in the orthogonal symmetryclass. This method employs a virtual lattice characterised by an arbitraryspectral dimension instead of a concrete lattice with a given integer or fractal dimension.This method makes it possible to simulate numerically infinite size systemon a computer. Moreover, the computational complexity does not increaseexponentially as the dimensionality increases. Thus, we can avoid the curse ofdimensionality. Also, we can estimate the critical exponent numerically withoutresorting to the finite size scaling method often used in previous numerical studiesof critical phenomena.
Category: Condensed Matter

Graph Equations

Authors: Elmar Guseinov
Comments: Pages.

В данной статье приводится решение 83 проблем, формулировка которых близка к формулировке гипотезы грациозности деревьев. В частности, было найдено дерево T=(E,V) с инъективной разметкой рёбер h числами {1,...,|E|}, для которой нельзя указать инъективной разметки вершин f, так чтобы для каждого ребра ab∈E выполнялось условие |f(a)-f(b)|=h(ab). Для оптимизации процесса решения была написана соответствующая рекомендательная программа.

In this article, we solve 83 problems related to the graceful tree conjecture. In particular, we have found a tree T=(E,V) and injective edge labeling h:E→{1,...,|E|} such that there is no injective vertex labeling f with the property that |f(a)-f(b)|=h(ab) for all ab∈E. To optimize the solution process, a recommendation computer program was written.
Category: Condensed Matter

Along the Side of the Onsager's Solution, the Ekagi Language

Authors: Anindya Kumar Biswas
Comments: thirteen page plus supplementary materials

We continue to consult the Ekagi-Dutch-English-Indonesian Dictionary by J. Steltenpool. Here we count all the Ekagi entries initiating with a letter. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter. We find that the entries underlie a magnetisation curve. The magnetisation curve i.e. the graph of the reduced magnetisation vs the reduced temperature is the exact Onsager solution of the two dimensional Ising model in the the absence of external magnetic field.
Category: Condensed Matter