scholarly journals The ground state energy of the Edwards–Anderson spin glass model with a parallel tempering Monte Carlo algorithm

2009 ◽  
Vol 388 (14) ◽  
pp. 2821-2838 ◽  
Author(s):  
F. Romá ◽  
S. Risau-Gusman ◽  
A.J. Ramirez-Pastor ◽  
F. Nieto ◽  
E.E. Vogel
Keyword(s):  
Monte Carlo ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Monte Carlo Algorithm ◽  
Parallel Tempering ◽  
Spin Glass Model ◽  
Glass Model

On ℓp-Gaussian–Grothendieck Problem

2021 ◽  
Author(s):  
Wei-Kuo Chen ◽  
Arnab Sen
Keyword(s):  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Mean Field ◽  
Stability Estimates ◽  
Spin Glass Model ◽  
Maximum Value ◽  
Glass Model ◽  
Gaussian Orthogonal Ensemble

Abstract For $p\geq 1$ and $(g_{ij})_{1\leq i,j\leq n}$ being a matrix of i.i.d. standard Gaussian entries, we study the $n$-limit of the $\ell _p$-Gaussian–Grothendieck problem defined as $$\begin{align*} & \max\Bigl\{\sum_{i,j=1}^n g_{ij}x_ix_j: x\in \mathbb{R}^n,\sum_{i=1}^n |x_i|^p=1\Bigr\}. \end{align*}$$The case $p=2$ corresponds to the top eigenvalue of the Gaussian orthogonal ensemble; when $p=\infty $, the maximum value is essentially the ground state energy of the Sherrington–Kirkpatrick mean-field spin glass model and its limit can be expressed by the famous Parisi formula. In the present work, we focus on the cases $1\leq p<2$ and $2<p<\infty .$ For the former, we compute the limit of the $\ell _p$-Gaussian–Grothendieck problem and investigate the structure of the set of all near optimizers along with stability estimates. In the latter case, we show that this problem admits a Parisi-type variational representation and the corresponding optimizer is weakly delocalized in the sense that its entries vanish uniformly in a polynomial order of $n^{-1}$.

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy

Monte Carlo calculation of the ground-state energy of an optical polaron

1983 ◽  
Vol 28 (10) ◽  
pp. 5735-5738 ◽  
Author(s):  
W. Becker ◽  
B. Gerlach ◽  
H. Schliffke
Keyword(s):  
Monte Carlo ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Monte Carlo Calculation
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