Relaxations of the Max Cut Problem and Computation of Spin Glass Ground States

1998 ◽  
pp. 74-83
Author(s):  
Michael Jünger ◽  
Giovanni Rinaldi
Keyword(s):  
Spin Glass ◽  
Ground States ◽  
Max Cut Problem

scholarly journals AKLT models with quantum spin glass ground states

2010 ◽  
Vol 81 (17) ◽  
Author(s):  
C. R. Laumann ◽  
S. A. Parameswaran ◽  
S. L. Sondhi ◽  
F. Zamponi
Keyword(s):  
Spin Glass ◽  
Ground States ◽  
Quantum Spin

GROUND STATES IN THREE-DIMENSIONAL ±J EDWARDS–ANDERSON SPIN GLASSES WITH FREE BOUNDARIES

2000 ◽  
Vol 11 (03) ◽  
pp. 589-592
Author(s):  
FRAUKE LIERS ◽  
MICHAEL JÜNGER
Keyword(s):  
Spin Glass ◽  
Spin Glasses ◽  
State Energy ◽  
Infinite System ◽  
Three Dimensional ◽  
Finite Size ◽  
Ground States ◽  
Free Boundaries ◽  
Finite Size Corrections

By an exact calculation of the ground states for the ±J Edwards–Anderson spin glass, one can extrapolate the ground state energy to infinite system sizes. We calculate the exact ground states for the three-dimensional spin glass with free boundaries for system sizes up to 10 and fit different finite-size functions. We cannot decide, only from the quality of the fit, which fitting function to choose. Relying on the literature values for the extrapolated energy, we find the finite-size corrections to vary as 1/L.

SPIN GLASSES IN THE TRADING BOOK

2000 ◽  
Vol 03 (03) ◽  
pp. 537-540 ◽  
Author(s):  
I. KONDOR
Keyword(s):  
Standard Model ◽  
Spin Glass ◽  
Long Range ◽  
Financial Institutions ◽  
Spin Glasses ◽  
Ground States ◽  
Capital Adequacy ◽  
Nonlinear Constraints ◽  
The Standard Model ◽  
Np Complete

The standard model defined in the Capital Adequacy Directive issued by the EEC in 1993 imposes nonlinear constraints on certain parts of the trading portfolios of financial institutions. It is shown that an institution that complies with the rules of the standard model but wants to optimize its portfolio according to some internal criteria, such as minimizing the variance or the VaR, faces a computational problem equivalent to finding the ground states of a long range spin glass. This problem is known to be NP-complete, and to have exponentially many solutions which are extremely sensitive to any changes of the input parameters.

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