We simulated the Edwards-Anderson Ising spin glass model in three dimensions via the recently proposed multicanonical ensemble. Physical quantities such as energy density, specific heat and entropy are evaluated at all temperatures. We studied their finite-size scaling, as well as the zero-temperature limit to explore the ground-state properties. Our estimate of the ground-state entropy per spin is s 0 = 0.046 ÷ 0.002.

arXiv:cond-mat/9210005Europhysics Letters (EPL)Apr 1, 199338 citations

arXiv:cond-mat/0502605 · Journal of Statistical Physics

Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass

Ronald Fisch

Published Jul 25, 2006• 2 citations

arXiv HTML PDF

DOI: 10.1007/s10955-006-9164-1

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V^3

. The energy, entropy and other physical quantities are easily calculable at all temperatures from a single simulation. Their finite size scalings and the zero temperature limits are also explored.

The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for

L \times L

square lattices with

L \le 20

, and

x

= 0.25 and 0.5, where

x

is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. Under these conditions, almost all domain walls have an energy

E_{dw}

equal to 0 or 4. The probability distribution of the entropy,

S_{dw}

, is found to depend strongly on

E_{dw}

. The results for

S_{dw}

when

E_{dw} = 4

agree with the prediction of the droplet model. Our results for

S_{dw}

when

E_{dw} = 0

agree with those of Saul and Kardar. In addition, we find that the distributions do not appear to be Gaussian in that case. The special role of

E_{dw} = 0

domain walls is discussed, and the discrepancy between the prediction of Amoruso, Hartmann, Hastings and Moore and the result of Saul and Kardar is explained.