Journal of Applied Physics

Order parameter distribution of the random bond Ising ferromagnet with antiperiodic boundary conditions

R. E. Hetzel, R. N. Bhatt

Published Apr 15, 1991• 1 citation

Abstract

The two-dimensional random bond Ising ferromagnet with antiperiodic boundaries in one direction has been studied by Monte Carlo simulations. From the overlap distribution function P(q), the scaling behavior of P(q) near q=0 with linear dimension L has been obtained. In contrast to recent simulations of the four-dimensional Ising spin glass, our results are consistent with the predictions of the droplet model.

DOI: 10.1063/1.348087

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Journal of Applied Physics

Order parameter distribution of the random bond Ising ferromagnet with antiperiodic boundary conditions

R. E. Hetzel, R. N. Bhatt

Published Apr 15, 1991• 1 citation

Publisher

Abstract

DOI: 10.1063/1.348087

Related papers

Ground-state behavior of the three-dimensional ±J random-bond Ising model

Alexander K. Hartmann

Large numbers of ground states of the three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ random-bond Ising model are calculated for sizes up to ${14}^{3}$ using a combination of a genetic algorithm and cluster-exact approximation. Several quantities are calculated as functions of the concentration p of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of ${p}_{c}=0.222\ifmmode\pm\else\textpm\fi{}0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents \ensuremath{\nu}=1.1\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\beta}=0.2\ifmmode\pm\else\textpm\fi{}0.1 are calculated. The behavior of the distribution of overlaps $P(q)$ is used to investigate how the spin-glass phase evolves with increasing concentration $p.$ The spin-glass order is characterized by a broad distribution of overlaps which extends down to $q=0.$ Large numbers of ground states of the three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ random-bond Ising model are calculated for sizes up to ${14}^{3}$ using a combination of a genetic algorithm and cluster-exact approximation. Several quantities are calculated as functions of the concentration p of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of ${p}_{c}=0.222\ifmmode\pm\else\textpm\fi{}0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents \ensuremath{\nu}=1.1\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\beta}=0.2\ifmmode\pm\else\textpm\fi{}0.1 are calculated. The behavior of the distribution of overlaps $P(q)$ is used to investigate how the spin-glass phase evolves with increasing concentration $p.$ The spin-glass order is characterized by a broad distribution of overlaps which extends down to $q=0.$

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Domain-wall energies and magnetization of the two-dimensional random-bond Ising model

Carlo Amoruso, Alexander K. Hartmann

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p∊[0,1]$ of antiferromagnetic and $(1\ensuremath{-}p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to $700$ . We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at ${p}_{c}\ensuremath{\sim}0.103$ compared to the concentration ${p}_{n}\ensuremath{\sim}0.109$ at the Nishimori point, which means that the phase diagram of the model exhibits a re-entrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p∊[0,1]$ of antiferromagnetic and $(1\ensuremath{-}p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to $700$. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at ${p}_{c}\ensuremath{\sim}0.103$ compared to the concentration ${p}_{n}\ensuremath{\sim}0.109$ at the Nishimori point, which means that the phase diagram of the model exhibits a re-entrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.

arXiv:cond-mat/0401464Physical Review BOct 29, 200448 citations

Large numbers of ground states of the three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ random-bond Ising model are calculated for sizes up to

{14}^{3}

using a combination of a genetic algorithm and cluster-exact approximation. Several quantities are calculated as functions of the concentration p of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of ${p}_{c}=0.222\ifmmode\pm\else\textpm\fi{}0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents \ensuremath{\nu}=1.1\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\beta}=0.2\ifmmode\pm\else\textpm\fi{}0.1 are calculated. The behavior of the distribution of overlaps

P(q)

is used to investigate how the spin-glass phase evolves with increasing concentration

p.

The spin-glass order is characterized by a broad distribution of overlaps which extends down to

q=0.

{\mathit{T}}_{\mathit{c}}

, the weight at small q seems to saturate to a nonzero value as the size increases, similar to the infinite-range Sherrington-Kirkpatrick model. We discuss our results in the light of recent theoretical predictions for the nature of the spin-glass phase.

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.

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration

p∊[0,1]

of antiferromagnetic and $(1\ensuremath{-}p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension

L

up to

700

. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at ${p}_{c}\ensuremath{\sim}0.103$ compared to the concentration ${p}_{n}\ensuremath{\sim}0.109$ at the Nishimori point, which means that the phase diagram of the model exhibits a re-entrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.