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

Result code in 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>

Result on the web

<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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Result language

angličtina

Original language name

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

Original language description

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

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

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Volume of the periodical

2015

Issue of the periodical within the volume

22

Country of publishing house

US - UNITED STATES

Number of pages

20

Pages from-to

1-20

UT code for WoS article

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EID of the result in the Scopus database

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