scholarly journals Fluctuations for the partition function of Ising models on Erdös–Rényi random graphs

2021 ◽  
Vol 57 (4) ◽  
Author(s):  
Zakhar Kabluchko ◽  
Matthias Löwe ◽  
Kristina Schubert
Keyword(s):  
Partition Function ◽  
Random Graphs ◽  
Ising Models

Fluctuations of the Magnetization for Ising Models on Dense Erdős–Rényi Random Graphs

2019 ◽  
Vol 177 (1) ◽  
pp. 78-94 ◽  
Author(s):  
Zakhar Kabluchko ◽  
Matthias Löwe ◽  
Kristina Schubert
Keyword(s):  
Random Graphs ◽  
Ising Models

scholarly journals Partition function of nearest neighbour Ising models: Some new insights

2009 ◽  
Vol 121 (5) ◽  
pp. 595-599 ◽  
Author(s):  
G. Nandhini ◽  
M. V. Sangaranarayanan
Keyword(s):  
Partition Function ◽  
Ising Models ◽  
Nearest Neighbour

scholarly journals Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 162 ◽  
Author(s):  
Ryan L. Mann ◽  
Michael J. Bremner
Keyword(s):  
Partition Function ◽  
Approximation Scheme ◽  
Ising Models ◽  
Quantum Circuits ◽  
Bounded Degree ◽  
Graph Polynomials ◽  
Bounded Degree Graphs ◽  
Complex Zeros ◽  
Complex Valued ◽  
Output Probability

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing the leading coefficients of graph polynomials on bounded degree graphs. Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum circuits.

scholarly journals Missing mass approximations for the partition function of stimulus driven Ising models

2013 ◽  
Vol 7 ◽  
Author(s):  
Robert Haslinger ◽  
Demba Ba ◽  
Ralf Galuske ◽  
Ziv Williams ◽  
Gordon Pipa
Keyword(s):  
Partition Function ◽  
Ising Models ◽  
Missing Mass
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