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

FRUSTRATED TRANSVERSE ISING MODELS: A CLASS OF FRUSTRATED QUANTUM SYSTEMS

1992 ◽  
Vol 06 (14) ◽  
pp. 2439-2469 ◽  
Author(s):  
P. SEN ◽  
B. K. CHAKRABARTI
Keyword(s):  
Excited States ◽  
Transverse Field ◽  
Ising Models ◽  
Quantum Systems ◽  
Nearest Neighbour ◽  
Competing Interactions ◽  
Annni Model ◽  
Kirkpatrick Model ◽  
Transverse Fields ◽  
Exact Diagonalisation

The analytical and numerical (Monte Carlo and exact diagonalisation) estimates of phase diagrams of frustrated Ising models in transverse fields are discussed here. Specifically we discuss the Sherrington–Kirkpatrick model in transverse field and the Axial Next-Nearest Neighbour Ising (ANNNI) model in transverse field. The effects of quantum fluctuations (induced by the transverse field) on the ground and excited states of such systems with competing interactions (frustration) are also discussed. The results are compared to those available for other frustrated quantum systems.

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

Zeros of the partition function of Ising models on fractal lattices

1987 ◽  
Vol 35 (10) ◽  
pp. 5036-5042 ◽  
Author(s):  
B. W. Southern ◽  
M. Kneević
Keyword(s):  
Partition Function ◽  
Ising Models
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