arXiv:1501.01165 · Physical Review E

Nonequilibrium random-field Ising model on a diluted triangular lattice

Lobisor Kurbah, Diana Thongjaomayum, Prabodh Shukla

Published Jan 16, 2015• 18 citations

Abstract

We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number ${z}_{\mathrm{eff}}$ in the range $3\ensuremath{\le}{z}_{\mathrm{eff}}\ensuremath{\le}6$. We find that the model supports critical behavior in the range $4<{z}_{\mathrm{eff}}\ensuremath{\le}6$, but the critical exponents are independent of ${z}_{\mathrm{eff}}$. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.

DOI: 10.1103/physreve.91.012131

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arXiv:1501.01165 · Physical Review E

Nonequilibrium random-field Ising model on a diluted triangular lattice

Lobisor Kurbah, Diana Thongjaomayum, Prabodh Shukla

Published Jan 16, 2015• 18 citations

arXiv HTML PDF

Abstract

We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number

{z}_{\mathrm{eff}}

in the range

3\ensuremath{\le}{z}_{\mathrm{eff}}\ensuremath{\le}6

. We find that the model supports critical behavior in the range

4<{z}_{\mathrm{eff}}\ensuremath{\le}6

, but the critical exponents are independent of

{z}_{\mathrm{eff}}

. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.

DOI: 10.1103/physreve.91.012131

Related papers

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We study the nonequilibrium critical point of the zero-temperature random-field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random-field Ising model belong to the same universality class. The physics of this curious result is not fully understood.We study the nonequilibrium critical point of the zero-temperature random-field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random-field Ising model belong to the same universality class. The physics of this curious result is not fully understood.

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We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

arXiv:1711.07981Physical review. EFeb 28, 201810 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

We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number

{z}_{\mathrm{eff}}

in the range

3\ensuremath{\le}{z}_{\mathrm{eff}}\ensuremath{\le}6

. We find that the model supports critical behavior in the range

4<{z}_{\mathrm{eff}}\ensuremath{\le}6

, but the critical exponents are independent of

{z}_{\mathrm{eff}}

. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.

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.