scholarly journals Lee-Yang zeros and the complexity of the ferromagnetic Ising Model on bounded-degree graphs

2021 ◽  
pp. 1508-1519
Author(s):  
Pjotr Buys ◽  
Andreas Galanis ◽  
Viresh Patel ◽  
Guus Regts
Keyword(s):  
Ising Model ◽  
Bounded Degree ◽  
Ferromagnetic Ising Model ◽  
Bounded Degree Graphs

scholarly journals A short note on conflict‐free coloring on closed neighborhoods of bounded degree graphs

2021 ◽  
Author(s):  
Sriram Bhyravarapu ◽  
Subrahmanyam Kalyanasundaram ◽  
Rogers Mathew
Keyword(s):  
Short Note ◽  
Bounded Degree ◽  
Bounded Degree Graphs

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.

scholarly journals EMBEDDING SPANNING BOUNDED DEGREE GRAPHS IN RANDOMLY PERTURBED GRAPHS

Mathematika ◽  
2020 ◽  
Vol 66 (2) ◽  
pp. 422-447 ◽  
Author(s):  
Julia Böttcher ◽  
Richard Montgomery ◽  
Olaf Parczyk ◽  
Yury Person
Keyword(s):  
Bounded Degree ◽  
Bounded Degree Graphs
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