Graphs critically embedded on Riemann surfaces and Ihara-Selberg zeta functions: genus one case

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10289597" target="_blank" >RIV/00216208:11320/15:10289597 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p10/pdf" target="_blank" >http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p10/pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Graphs critically embedded on Riemann surfaces and Ihara-Selberg zeta functions: genus one case

Popis výsledku v původním jazyce

The aim of the paper is to formulate a discrete analogue of the claim made by Alvarez-Gaume et al., (cite{a}), realizing the partition function of the free fermion on a closed Riemann surface of genus $g$ as a linear combination of $2^{2g}$ Pfaffians ofDirac operators. Let $G=(V,E)$ be a finite graph embedded in a closed Riemann surface $X$ of genus $g$, $x_e$ the collection of independent variables associated with each edge $e$ of $G$ (collected in one vector variable $x$) and $S$ the set of all $2^{2g}$ Spin-structures on $X$. We introduce $2^{2g}$ rotations $rot_s$ and $(2|E|times 2|E|)$ matrices $D(s)(x)$, $sin S$, of the transitions between the oriented edges of $G$ determined by rotations $rot_s$. We show that the generating function for the even subsets of edges of $G$, i.e., the Ising partition function, is a linear combination of the square roots of $2^{2g}$ Ihara-Selberg functions $I(D(s)(x))$ also called Feynman functions. By a result of Foata--Zeilberger holds $I(D

Název v anglickém jazyce

Graphs critically embedded on Riemann surfaces and Ihara-Selberg zeta functions: genus one case

Popis výsledku anglicky

The aim of the paper is to formulate a discrete analogue of the claim made by Alvarez-Gaume et al., (cite{a}), realizing the partition function of the free fermion on a closed Riemann surface of genus $g$ as a linear combination of $2^{2g}$ Pfaffians ofDirac operators. Let $G=(V,E)$ be a finite graph embedded in a closed Riemann surface $X$ of genus $g$, $x_e$ the collection of independent variables associated with each edge $e$ of $G$ (collected in one vector variable $x$) and $S$ the set of all $2^{2g}$ Spin-structures on $X$. We introduce $2^{2g}$ rotations $rot_s$ and $(2|E|times 2|E|)$ matrices $D(s)(x)$, $sin S$, of the transitions between the oriented edges of $G$ determined by rotations $rot_s$. We show that the generating function for the even subsets of edges of $G$, i.e., the Ising partition function, is a linear combination of the square roots of $2^{2g}$ Ihara-Selberg functions $I(D(s)(x))$ also called Feynman functions. By a result of Foata--Zeilberger holds $I(D

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

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Svazek periodika

2015

Číslo periodika v rámci svazku

22

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

1-20

Kód UT WoS článku

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EID výsledku v databázi Scopus

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