GROUND STATES FOR LARGE SAMPLES OF TWO-DIMENSIONAL ISING SPIN GLASSES

1999 ◽  
Vol 10 (04) ◽  
pp. 667-675 ◽  
Author(s):  
R. G. PALMER ◽  
JOAN ADLER
Keyword(s):  
Spin Glasses ◽  
Infinite System ◽  
Energy Estimate ◽  
Finite Size ◽  
Computer Time ◽  
Sample Length ◽  
Matching Method ◽  
Large Samples ◽  
Ising Spin ◽  
Groundstate Energy

We have developed a combinatoric matching method to find the exact groundstate energy for the 2-D Ising spin glass with the ± J distribution and equal numbers of positive and negative bonds. For the largest size (1800×1800 plaquettes of spins), we averaged results from 278 samples and for the smaller ones up to 374, 375 samples. We also studied the behavior of the distributions of computer time (CPU) and memory as functions of sample size. We present finite size scaling leading to a groundstate energy estimate of E∞=-1.40193±2 for the infinite system. We found that the memory scales as the square of sample length and that for a given size, the CPU time appears to have a skewed and high-tailed distribution.

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.

PHASE TRANSITIONS IN SPIN GLASSES

2009 ◽  
Vol 20 (09) ◽  
pp. 1411-1421
Author(s):  
A. P. YOUNG
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Spin Glass ◽  
Spin Glasses ◽  
Finite Size ◽  
Three Dimensions ◽  
Scaling Analysis ◽  
Zero Field ◽  
Exchange Method ◽  
Ising Spin

Some recent progress in Monte Carlo simulations of spin glasses will be presented. The problem of slow dynamics at low temperatures is partially alleviated by use of the parallel tempering (replica exchange) method. A useful technique to check for equilibration (applicable only for a Gaussian distribution) will be discussed. It will be argued that a finite size scaling analysis of the scaled correlation length of the system is a good approach with which to investigate phase transitions in spin glasses. This method will be used to study two questions: (i) whether there is a phase transition in zero field in the Heisenberg spin glass in three dimensions, and (ii) whether there is phase transition in a magnetic field in an Ising spin glass, also in three dimensions.

scholarly journals Finite-size critical scaling in Ising spin glasses in the mean-field regime

2016 ◽  
Vol 93 (3) ◽  
Author(s):  
T. Aspelmeier ◽  
Helmut G. Katzgraber ◽  
Derek Larson ◽  
M. A. Moore ◽  
Matthew Wittmann ◽  
...  
Keyword(s):  
Spin Glasses ◽  
Mean Field ◽  
Finite Size ◽  
Critical Scaling ◽  
Ising Spin ◽  
The Mean ◽  
Mean Field Regime

RECENT DEVELOPMENTS IN ISING SPIN GLASSES

1996 ◽  
Vol 07 (03) ◽  
pp. 327-335 ◽  
Author(s):  
A. P. YOUNG ◽  
N. KAWASHIMA
Keyword(s):  
Transition Temperature ◽  
Spin Glasses ◽  
Three Dimensional ◽  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Ising Spin ◽  
Recent Developments ◽  
Rule Out

We have studied the three-dimensional Ising spin glass with a ± J distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, Tc, with ordering below Tc. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, ν, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that Tc = 0 or that Tc is finite but with no order below Tc. However, from our data, these possibilities seem less likely.

Finite size scaling in 3D Ising spin glasses

1999 ◽  
Vol 121-122 ◽  
pp. 180-182
Author(s):  
M. Palassini ◽  
S. Caracciolo
Keyword(s):  
Spin Glasses ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Ising Spin

Damage Spreading in ±J Asymmetric Ising Spin Glasses

1995 ◽  
Vol 5 (3) ◽  
pp. 355-364 ◽  
Author(s):  
R. M.C. de Almeida ◽  
L. Bernadi ◽  
I. A. Campbell
Keyword(s):  
Spin Glasses ◽  
Damage Spreading ◽  
Ising Spin
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