scholarly journals Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

2016 ◽  
Vol 94 (13) ◽  
Author(s):  
Wenxuan Huang ◽  
Daniil A. Kitchaev ◽  
Stephen T. Dacek ◽  
Ziqin Rong ◽  
Alexander Urban ◽  
...  
Keyword(s):  
Ising Model ◽  
Convex Optimization ◽  
Ground State ◽  
Exact Ground State ◽  
Max Sat ◽  
Generalized Ising Model

scholarly journals Order-Disorder Phenomena in Complex Alloys: The Case of A15-Based Substitutional Alloys

1990 ◽  
Vol 186 ◽  
Author(s):  
P.E.A. Turchi ◽  
A. Finel
Keyword(s):  
Ising Model ◽  
Perturbation Method ◽  
Ground State ◽  
Experimental Situation ◽  
Statistical Techniques ◽  
Stability Properties ◽  
The Stability ◽  
Substitutional Alloys ◽  
Pair Interactions ◽  
Generalized Ising Model

AbstractWe first discuss the applicability of the Generalized Perturbation Method to the study of ordering phenomena in complex alloys for which stability properties are electronically driven. In particular, according to previous work, it is recalled that a 3D-generalized Ising model is appropriate to address the problem of configurational order in A 15-based substitutional alloys. A ground state analysis of this model, including 1st, 2nd and weak 3rd and 7th pair interactions, generates two new ordered states at the composition A5B3 and A7B, apart from the well known A3B configuration. The stability of these predicted configurations is examined as a function of temperature and concentration by means of standard statistical techniques. The results are discussed in relation with the experimental situation.

Exact Ground State Solution for Anyons with spin-$\frac {1}{2}$

1992 ◽  
Vol 17 (1) ◽  
pp. 107-110
Author(s):  
Shun-Qing Shen ◽  
J. Cai ◽  
Rui-Bao Tao
Keyword(s):  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
Exact Ground State

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

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