Separation of the Interaction Potential into Two Parts in Statistical Mechanics. II. Graph Theory for Lattice Gases and Spin Systems with Application to Systems with Long‐Range Potentials

1966 ◽  
Vol 7 (8) ◽  
pp. 1532-1547 ◽  
Author(s):  
G. Stell ◽  
J. L. Lebowitz ◽  
S. Baer ◽  
W. Theumann
Keyword(s):  
Graph Theory ◽  
Statistical Mechanics ◽  
Long Range ◽  
Interaction Potential ◽  
Spin Systems ◽  
Lattice Gases

Construction of Integrable Spin Systems with Long-Range Interactions

1992 ◽  
Vol 61 (9) ◽  
pp. 3071-3076 ◽  
Author(s):  
Kazuhiro Hikami ◽  
P. P. Kulish ◽  
Miki Wadati
Keyword(s):  
Long Range ◽  
Spin Systems ◽  
Long Range Interactions ◽  
Integrable Spin

Fast decay of eigenfunction correlators in long-range continuous random alloys

2019 ◽  
Vol 27 (1) ◽  
pp. 43-51
Author(s):  
Victor Chulaevsky
Keyword(s):  
Long Range ◽  
Exponential Decay ◽  
Interaction Potential ◽  
Dynamical Localization ◽  
Fast Decay ◽  
Euclidean Spaces ◽  
Strong Disorder ◽  
Low Energies ◽  
Media Interaction ◽  
Random Alloys

Abstract We study random Anderson Hamiltonians in Euclidean spaces with a long-range particle-media interaction potential {\mathfrak{u}(r)=r^{-A}} . Improving earlier results, for any {A>2d} , we establish spectral and strong dynamical localization with sub-exponential decay of eigenfunction correlators, both in the strong disorder regime and at low energies.

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