Thermodynamical Averages For The Ising Model And Spectral Invariants Of Toeplitz Matrices

2020 ◽  
Vol 203 (3) ◽  
pp. 780-793
Author(s):  
V. M. Kaplitsky
Keyword(s):  
Ising Model ◽  
Toeplitz Matrices ◽  
Spectral Invariants

scholarly journals Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Walter Vinci ◽  
Klas Markström ◽  
Sergio Boixo ◽  
Aidan Roy ◽  
Federico M. Spedalieri ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Ising Model ◽  
Partition Function ◽  
Low Energy ◽  
Partition Functions ◽  
Spectral Invariants ◽  
Physical Systems ◽  
Energy States ◽  
Isomorphic Graphs ◽  
Quantum Spectra

Abstract Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.

SPIN ONE ISING MODEL WITH COMPETING INTERACTIONS ON THE BETHE LATTICE

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1031-C8-1032
Author(s):  
S. Coutinho ◽  
C. R. da Silva
Keyword(s):  
Ising Model ◽  
Bethe Lattice ◽  
Competing Interactions

CRITICAL DYNAMICS OF THE ISING MODEL WITH ISING MACHINE

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1397-C8-1398 ◽  
Author(s):  
N. Ito ◽  
M. Taiji ◽  
M. Suzuki
Keyword(s):  
Ising Model ◽  
Critical Dynamics

Dipole Ising model for the crystals of Sn2P2S6 family

1999 ◽  
Vol 4 (0) ◽  
pp. 112-119
Author(s):  
О. В. Дробнич ◽  
Ю. М. Височанський
Keyword(s):  
Ising Model
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