arXiv:cond-mat/0009029 · Brazilian Journal of Physics

Experimental characterization of the Ising model in disordered antiferromagnets

David Peter Belanger

Published Dec 1, 2000• 67 citations

Abstract

The current status of experiments on the d = 2 and d = 3 random-exchange and random-field Ising models, as realized in dilute anisotropic antiferromagnets, is discussed. Two areas of current investigation are emphasized. For d = 3, the large random field limit is investigated and equilibrium critical behavior is characterized at high magnetic concentrations.

DOI: 10.1590/s0103-97332000000400009

Related papers

EXPERIMENTS ON THE RANDOM FIELD ISING MODEL

David Peter Belanger

arXiv:cond-mat/9706042Series on directions in condensed matter physicsDec 1, 199725 citations

Phase diagrams of the diluted and random-bond Ising model

Ligia Edith Zamora, German Antonio Pérez Alcázar, Alberto Bohorquez +2 more

The quenched-bond disordered Ising model is studied by means of the mean-field renormalization-group approach. Besides dilution and ferromagnetic random bond, the probability distribution function also includes two extra competing random bonds which can be ferromagnetic or antiferromagnetic, depending on the sign of some competing parameters. The critical temperature against ferromagnetic bond concentration phase diagrams are analyzed for several values of the theoretical parameters.

Physical review. B, Condensed matterApr 1, 199523 citations

Critical properties of a dilute Ising model in the percolation limit

J. Heinrichs

Physical review. B, Condensed matterAug 1, 19781 citation

Crossover from random-exchange to random-field critical behavior in Ising models

Pasquale Calabrese, Andrea Pelissetto C, Ettore Vicari

arXiv:cond-mat/0305041Physical review. B, Condensed matterSep 24, 20038 citations

Phase transformations in the disordered antiferromagnetic Ising model

Vladimir V. Prudnikov, O. N. Markov, E. V. Osintsev

Journal of Experimental and Theoretical PhysicsSep 1, 19990 citations

Numerical results for the random-field Ising model and the dilute antiferromagnetic Ising model in a uniform field

Julio F. Fernández, Erling Pytte

Physical review. B, Condensed matterMar 1, 19858 citations

arXiv:cond-mat/0009029 · Brazilian Journal of Physics

Experimental characterization of the Ising model in disordered antiferromagnets

David Peter Belanger

Published Dec 1, 2000• 67 citations

arXiv HTML PDF

Abstract

DOI: 10.1590/s0103-97332000000400009

Related papers

EXPERIMENTS ON THE RANDOM FIELD ISING MODEL

David Peter Belanger

New advances in experiments on the random-field Ising model, as realized in dilute antiferromagnets, have brought us much closer to a full characterization of the static and dynamic critical behavior of the unusual phase transition in three dimensions (d=3). The most important experiments that have laid the ground work for our present understanding are reviewed. Comparisons of the data with Monte Carlo simulations of the d=3 critical behavior are made. We review the current experimental understanding of the destroyed d=2 transition and the experiments exploring the d=2 metastability at low T. Connections to theories most relevant to the interpretations of all the experiments are discussed.New advances in experiments on the random-field Ising model, as realized in dilute antiferromagnets, have brought us much closer to a full characterization of the static and dynamic critical behavior of the unusual phase transition in three dimensions (d=3). The most important experiments that have laid the ground work for our present understanding are reviewed. Comparisons of the data with Monte Carlo simulations of the d=3 critical behavior are made. We review the current experimental understanding of the destroyed d=2 transition and the experiments exploring the d=2 metastability at low T. Connections to theories most relevant to the interpretations of all the experiments are discussed.

arXiv:cond-mat/9706042Series on directions in condensed matter physicsDec 1, 199725 citations

Phase diagrams of the diluted and random-bond Ising model

Ligia Edith Zamora, German Antonio Pérez Alcázar, Alberto Bohorquez +2 more

Physical review. B, Condensed matterApr 1, 199523 citations

Critical properties of a dilute Ising model in the percolation limit

J. Heinrichs

The critical behavior of the dilute Ising model on a Bethe lattice of coordination $z$ is studied in the percolation limit ($T\ensuremath{\rightarrow}0$) by means of a new moment-expansion procedure. Exact numerical results for the magnetization as a function of magnetic field at the critical concentration, $p={p}_{c}$ , are presented for $z=3$ and $z=4$ . In particular, the critical exponent ${\ensuremath{\delta}}_{P}$ is expected to agree well for very low fields with the approximate value ${\ensuremath{\delta}}_{P}=2$ obtained by Essam et al. The nature of deviations from the value ${\ensuremath{\delta}}_{P}=2$ is discussed and their consequences are noted. The case $p\ensuremath{\ne}{p}_{c}$ is also discussed.The critical behavior of the dilute Ising model on a Bethe lattice of coordination $z$ is studied in the percolation limit ($T\ensuremath{\rightarrow}0$) by means of a new moment-expansion procedure. Exact numerical results for the magnetization as a function of magnetic field at the critical concentration, $p={p}_{c}$, are presented for $z=3$ and $z=4$. In particular, the critical exponent ${\ensuremath{\delta}}_{P}$ is expected to agree well for very low fields with the approximate value ${\ensuremath{\delta}}_{P}=2$ obtained by Essam et al. The nature of deviations from the value ${\ensuremath{\delta}}_{P}=2$ is discussed and their consequences are noted. The case $p\ensuremath{\ne}{p}_{c}$ is also discussed.

Physical review. B, Condensed matterAug 1, 19781 citation

Crossover from random-exchange to random-field critical behavior in Ising models

Pasquale Calabrese, Andrea Pelissetto C, Ettore Vicari

We compute the crossover exponent $\ensuremath{\varphi}$ describing the crossover from the random-exchange to the random-field critical behavior in Ising systems. For this purpose, we consider the field-theoretical approach based on the replica method, and perform a six-loop calculation in the framework of a fixed-dimension expansion. The crossover from random-exchange to random-field critical behavior has been observed in dilute anisotropic antiferromagnets, such as ${\mathrm{Fe}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$ and ${\mathrm{Mn}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2},$ when applying an external magnetic field. Our result $\ensuremath{\varphi}=1.42(2)$ for the crossover exponent is in good agreement with the available experimental estimates.We compute the crossover exponent $\ensuremath{\varphi}$ describing the crossover from the random-exchange to the random-field critical behavior in Ising systems. For this purpose, we consider the field-theoretical approach based on the replica method, and perform a six-loop calculation in the framework of a fixed-dimension expansion. The crossover from random-exchange to random-field critical behavior has been observed in dilute anisotropic antiferromagnets, such as ${\mathrm{Fe}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$ and ${\mathrm{Mn}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2},$ when applying an external magnetic field. Our result $\ensuremath{\varphi}=1.42(2)$ for the crossover exponent is in good agreement with the available experimental estimates.

arXiv:cond-mat/0305041Physical review. B, Condensed matterSep 24, 20038 citations

Phase transformations in the disordered antiferromagnetic Ising model

Vladimir V. Prudnikov, O. N. Markov, E. V. Osintsev

We employ the Monte Carlo method to provide a computer description of the thermodynamic properties of the disordered antiferromagnetic Ising model for a simple cubic lattice with allowance for the nearest neighbors interaction and the next-nearest neighbors interaction. We construct the phase diagram for the model in an external magnetic field for systems with spin concentrations p =1.0, 0.95, and 0.8. We also establish the tricritical behavior of the model. Finally, we study the critical behavior of the model in weak fields.We employ the Monte Carlo method to provide a computer description of the thermodynamic properties of the disordered antiferromagnetic Ising model for a simple cubic lattice with allowance for the nearest neighbors interaction and the next-nearest neighbors interaction. We construct the phase diagram for the model in an external magnetic field for systems with spin concentrations p =1.0, 0.95, and 0.8. We also establish the tricritical behavior of the model. Finally, we study the critical behavior of the model in weak fields.

Journal of Experimental and Theoretical PhysicsSep 1, 19990 citations

Numerical results for the random-field Ising model and the dilute antiferromagnetic Ising model in a uniform field

Julio F. Fernández, Erling Pytte

We have studied the equilibrium properties of the random-field (H) ferromagnetic Ising model (RFIM) and the dilute antiferromagnetic Ising model (DAF) in a uniform field. For RFIM we have used the transfer-matrix technique, thus bypassing serious equilibration problems which would arise in a Monte Carlo calculation for random systems. We have calculated the structure factor S versus H. Our results are consistent with S\ensuremath{\sim}exp(c/ ${H}^{2}$ ) as predicted by theories which yield a lower critical dimension ${d}_{c}$ =2, whereas the expected behavior for ${d}_{c}$ =3, S\ensuremath{\sim}${H}^{\mathrm{\ensuremath{-}}4}$ is inconsistent with our results. We have carried out analogous calculations for DAF. Our results for DAF suffer seriously from finite-size effects. To circumvent this difficulty, we have also performed calculations on interface models. Together, these results indicate that DAF crosses over to RFIM behavior at H\ensuremath{\simeq}J.We have studied the equilibrium properties of the random-field (H) ferromagnetic Ising model (RFIM) and the dilute antiferromagnetic Ising model (DAF) in a uniform field. For RFIM we have used the transfer-matrix technique, thus bypassing serious equilibration problems which would arise in a Monte Carlo calculation for random systems. We have calculated the structure factor S versus H. Our results are consistent with S\ensuremath{\sim}exp(c/${H}^{2}$) as predicted by theories which yield a lower critical dimension ${d}_{c}$=2, whereas the expected behavior for ${d}_{c}$=3, S\ensuremath{\sim}${H}^{\mathrm{\ensuremath{-}}4}$ is inconsistent with our results. We have carried out analogous calculations for DAF. Our results for DAF suffer seriously from finite-size effects. To circumvent this difficulty, we have also performed calculations on interface models. Together, these results indicate that DAF crosses over to RFIM behavior at H\ensuremath{\simeq}J.

Physical review. B, Condensed matterMar 1, 19858 citations

The critical behavior of the dilute Ising model on a Bethe lattice of coordination

z

is studied in the percolation limit ($T\ensuremath{\rightarrow}0$) by means of a new moment-expansion procedure. Exact numerical results for the magnetization as a function of magnetic field at the critical concentration,

p={p}_{c}

, are presented for

z=3

and

z=4

. In particular, the critical exponent ${\ensuremath{\delta}}_{P}$ is expected to agree well for very low fields with the approximate value ${\ensuremath{\delta}}_{P}=2$ obtained by Essam et al. The nature of deviations from the value ${\ensuremath{\delta}}_{P}=2$ is discussed and their consequences are noted. The case $p\ensuremath{\ne}{p}_{c}$ is also discussed.

{H}^{2}

) as predicted by theories which yield a lower critical dimension

{d}_{c}

=2, whereas the expected behavior for

{d}_{c}

=3, S\ensuremath{\sim}${H}^{\mathrm{\ensuremath{-}}4}$ is inconsistent with our results. We have carried out analogous calculations for DAF. Our results for DAF suffer seriously from finite-size effects. To circumvent this difficulty, we have also performed calculations on interface models. Together, these results indicate that DAF crosses over to RFIM behavior at H\ensuremath{\simeq}J.