Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Fluctuations in the Curie-Weiss Version of the Ising Model with Random Field

João Amaro de Matos, J. Fernando Perez

Published Apr 1, 1992• 3 citations
Publisher

Abstract

For the Curie-Weiss version of the Ising Model with random field it is shown that the fluctuations have: i) a Gaussian distribution with random (i. e. sample dependent) mean, if the system is away from criticality or at first-order critical points; ii) a sample-independent non-Gaussian distribution at second- or higher-order critical points.

DOI
10.1209/0295-5075/18/7/015

Related papers

Fluctuations in the Curie-Weiss Version of the Ising Model with Random Field

João Amaro de Matos, J. Fernando Perez

For the Curie-Weiss version of the Ising Model with random field it is shown that the fluctuations have: i) a Gaussian distribution with random ( i. e. sample dependent) mean, if the system is away from criticality or at first-order critical points; ii) a sample-independent non-Gaussian distribution at second- or higher-order critical points.

Europhysics Letters (EPL)•Feb 1, 1988•4 citations

Fluctuations in dilute antiferromagnets: Curie-Weiss models

João Amaro de Matos, J. A. Baêta Segundo, J F Perez

The authors compute the fluctuations of the order parameter in the Curie-Weiss version of a site-dilute antiferromagnet. Their results show: (i) Gaussian fluctuations away from criticality or at a first-order critical point with sample and thermal fluctuations contributing in same order; (ii) Non-Gaussian fluctuations with critical exponents modified by the presence of dilution at the second-order critical point. In this case sample-induced fluctuations are enhanced to dominate over the thermal ones. Critical exponents are the same as in the Curie-Weiss random field Ising model.

Journal of Physics A Mathematical and General•May 21, 1992•3 citations

Ferromagnetism

Lawrence S. Schulman

Abstract Magnetism and order parameters are discussed in both mean field theory and exact treatments. An example of stochastic dynamics for the Ising model is given. The Curie–Weiss model is defined as a system in which mean field theory is exact. For this system (consisting of N spins) the fluctuations at the critical point are the fourth root of N, rather than the square root as is the case when the variables are independent.

•Jan 18, 2022•0 citations

Fluctuations and criticality in the random-field Ising model

Panagiotis E. Theodorakis, Ioannis Georgiou, Nikolaos G. Fytas

We investigate the critical properties of the $d=3$ random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength $h$ and system sizes $\mathcal{V}=L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$, with $L\ensuremath{\le}156$. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength ${h}_{\mathrm{c}}$ and the correlation length exponent $\ensuremath{\nu}$. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent $\ensuremath{\alpha}$ and the violation of the hyperscaling exponent $\ensuremath{\theta}$. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios $\ensuremath{\beta}/\ensuremath{\nu}$ and $\overline{\ensuremath{\gamma}}/\ensuremath{\nu}$, respectively.

Physical Review E•Mar 8, 2013•11 citations

High-temperature series and the random-field Ising model

A. Houghton, Anil Khurana, F. J. Seco

A formalism is given whereby high-temperature series for the random-field Ising model are obtained by partitioning the vertices of the pure Ising series' diagrams; for any given order in the high-temperature variable, the random fields are thereby treated exactly. Series for the susceptibility up to seventh order in the high-temperature variable have been obtained for an arbitrary distribution of the random fields. Series for a bimodal and a Gaussian distribution were analyzed by Dlog-Pad\'e methods. The analysis predicts that, for a bimodal distribution of random fields, the tricritical point predicted by mean-field theory persists in all dimensions above the lower critical dimension, but moves to weaker fields as the dimension is reduced. For the Gaussian distribution, the transition is predicted to be second order over the whole phase boundary for dimension d\ensuremath{\ge}4; however, for d<4 the analysis suggests that fluctuations drive the transition first order for sufficiently strong fields implying that d=4 is a ``critical'' dimension for this model. Above four dimensions the value of the susceptibility exponent determined from the series is consistent with the predictions of the d\ensuremath{\rightarrow}d-2 rule for both distributions.

Physical review. B, Condensed matter•Aug 1, 1986•26 citations

Mean-field phase diagram of the spin-1 Ising ferromagnet in a Gaussian random crystal field

C. E. I. Carneiro, Vera B. Henriques, Silvio R. A. Salinas

The authors consider the mean-field version of a spin-1 Ising ferromagnet in a random crystal field described by a Gaussian probability distribution. Depending on the width of the Gaussian, they obtain a rich phase diagram, with critical and coexistence lines and some multicritical points. At low temperatures, their numerical results are supported by some analytic asymptotic expansions. They also calculate the ground state for a suitable two-valued delta-function distribution to compare with the results for the Gaussian case.

Journal of Physics A Mathematical and General•Jul 21, 1990•26 citations
For the Curie-Weiss version of the Ising Model with random field it is shown that the fluctuations have: i) a Gaussian distribution with random (i. e. sample dependent) mean, if the system is away from criticality or at first-order critical points; ii) a sample-independent non-Gaussian distribution at second- or higher-order critical points.
The authors compute the fluctuations of the order parameter in the Curie-Weiss version of a site-dilute antiferromagnet. Their results show: (i) Gaussian fluctuations away from criticality or at a first-order critical point with sample and thermal fluctuations contributing in same order; (ii) Non-Gaussian fluctuations with critical exponents modified by the presence of dilution at the second-order critical point. In this case sample-induced fluctuations are enhanced to dominate over the thermal ones. Critical exponents are the same as in the Curie-Weiss random field Ising model.
We investigate the critical properties of the d=3d=3d=3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength hhh and system sizes $\mathcal{V}=L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$, with $L\ensuremath{\le}156$. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength hc{h}_{\mathrm{c}}hc​ and the correlation length exponent $\ensuremath{\nu}$. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent $\ensuremath{\alpha}$ and the violation of the hyperscaling exponent $\ensuremath{\theta}$. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios $\ensuremath{\beta}/\ensuremath{\nu}$ and $\overline{\ensuremath{\gamma}}/\ensuremath{\nu}$, respectively.
A formalism is given whereby high-temperature series for the random-field Ising model are obtained by partitioning the vertices of the pure Ising series' diagrams; for any given order in the high-temperature variable, the random fields are thereby treated exactly. Series for the susceptibility up to seventh order in the high-temperature variable have been obtained for an arbitrary distribution of the random fields. Series for a bimodal and a Gaussian distribution were analyzed by Dlog-Pad\'e methods. The analysis predicts that, for a bimodal distribution of random fields, the tricritical point predicted by mean-field theory persists in all dimensions above the lower critical dimension, but moves to weaker fields as the dimension is reduced. For the Gaussian distribution, the transition is predicted to be second order over the whole phase boundary for dimension d\ensuremath{\ge}4; however, for d<4 the analysis suggests that fluctuations drive the transition first order for sufficiently strong fields implying that d=4 is a ``critical'' dimension for this model. Above four dimensions the value of the susceptibility exponent determined from the series is consistent with the predictions of the d\ensuremath{\rightarrow}d-2 rule for both distributions.
The authors consider the mean-field version of a spin-1 Ising ferromagnet in a random crystal field described by a Gaussian probability distribution. Depending on the width of the Gaussian, they obtain a rich phase diagram, with critical and coexistence lines and some multicritical points. At low temperatures, their numerical results are supported by some analytic asymptotic expansions. They also calculate the ground state for a suitable two-valued delta-function distribution to compare with the results for the Gaussian case.