The Location of Zeros

1976 ◽  
pp. 212-251
Author(s):  
George Pólya ◽  
Gabor Szegö
Keyword(s):  
Location Of Zeros

scholarly journals Lee-Yang zeros of the antiferromagnetic Ising model

2021 ◽  
pp. 1-35
Author(s):  
FERENC BENCS ◽  
PJOTR BUYS ◽  
LORENZO GUERINI ◽  
HAN PETERS
Keyword(s):  
Ising Model ◽  
Partition Functions ◽  
Cayley Trees ◽  
Circular Arcs ◽  
Precise Characterization ◽  
Ferromagnetic Ising Model ◽  
Location Of Zeros ◽  
Antiferromagnetic Ising Model ◽  
Recursively Defined Trees ◽  
Degree Bound

Abstract We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

Location of Zeros

2019 ◽  
pp. 81-83
Author(s):  
Vittorino Pata
Keyword(s):  
Location Of Zeros

On the location of zeros of the Homfly polynomial

2011 ◽  
Vol 2011 (07) ◽  
pp. P07011 ◽  
Author(s):  
Xian’an Jin ◽  
Fuji Zhang
Keyword(s):  
Homfly Polynomial ◽  
Location Of Zeros

Location of Zeros of Chromatic and Related Polynomials of Graphs

1994 ◽  
Vol 46 (1) ◽  
pp. 55-80 ◽  
Author(s):  
Francesco Brenti ◽  
Gordon F. Royle ◽  
David G. Wagner
Keyword(s):  
Generating Functions ◽  
Sufficient Conditions ◽  
Combinatorial Identities ◽  
Chromatic Polynomials ◽  
Real Zeros ◽  
Location Of Zeros ◽  
Theoretical Results

AbstractWe consider the location of zeros of four related classes of polynomials, one of which is the class of chromatic polynomials of graphs. All of these polynomials are generating functions of combinatorial interest. Extensive calculations indicate that these polynomials often have only real zeros, and we give a variety of theoretical results which begin to explain this phenomenon. In the course of the investigation we prove a number of interesting combinatorial identities and also give some new sufficient conditions for a polynomial to have only real zeros.

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