The two-dimensional Ising model with two kinds of bonds –ferro and antiferromagnetic– is investigated in both quenched and annealed approximations. High temperature series expansion technique is used to get the respective free energies and susceptibilities. Form the analysis of the ratio method results, the phase diagrams are drawn and critical concentrations are estimated. It is shown that in both approximations the system behaves similarly, although in the annealed case the magnetically ordered phases are more stable against increasing impurity concentration. It is also proved that for Bethe lattices initial susceptibilities for quenced and annealed systems coincide.The two-dimensional Ising model with two kinds of bonds –ferro and antiferromagnetic– is investigated in both quenched and annealed approximations. High temperature series expansion technique is used to get the respective free energies and susceptibilities. Form the analysis of the ratio method results, the phase diagrams are drawn and critical concentrations are estimated. It is shown that in both approximations the system behaves similarly, although in the annealed case the magnetically ordered phases are more stable against increasing impurity concentration. It is also proved that for Bethe lattices initial susceptibilities for quenced and annealed systems coincide.

Progress of Theoretical PhysicsOct 1, 197514 citations

Thermodynamics of the two-dimensional random-bond Ising model

Creighton K. Thomas, Helmut G. Katzgraber

Bulletin of the American Physical SocietyMar 23, 20110 citations

Self-consistent approach for the two-dimensional Ising model with random bonds

Daniel Braak, K. Ziegler

The European Physical Journal BOct 1, 19923 citations

High-Temperature Series Analysis of 2D Random-Bond Ising Ferromagnets

Alexandra Roder, Joan Adler, Wolfhard Janke E

We analyze new high-temperature series expansions for the susceptibility $\ensuremath{\chi}$ of the two-dimensional random-bond Ising ferromagnet with a symmetric bimodal distribution of two positive couplings ${J}_{1}$ and ${J}_{2}$ . By studying a wide range of coupling ratios ${J}_{2}/{J}_{1}$ we obtain compelling evidence for a critical behavior of the form $\ensuremath{\chi}\ensuremath{\sim}{t}^{\ensuremath{-}7/4}|\mathrm{ln}t{|}^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig.We analyze new high-temperature series expansions for the susceptibility $\ensuremath{\chi}$ of the two-dimensional random-bond Ising ferromagnet with a symmetric bimodal distribution of two positive couplings ${J}_{1}$ and ${J}_{2}$. By studying a wide range of coupling ratios ${J}_{2}/{J}_{1}$ we obtain compelling evidence for a critical behavior of the form $\ensuremath{\chi}\ensuremath{\sim}{t}^{\ensuremath{-}7/4}|\mathrm{ln}t{|}^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig.

Physical Review LettersMay 25, 199840 citations

High-temperature series expansion for the relaxation times of the two dimensional Ising model

Bernd Dammann, Joseph D. Reger

The European Physical Journal BMar 1, 19957 citations

High-temperature series for the bond-diluted Ising model in 3, 4, and 5 dimensions

Meik Hellmund, Wolfhard Janke E

In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the susceptibility and the free energy are obtained for the quenched bond-diluted Ising model in $d=3--5$ dimensions. They are analyzed using different extrapolation methods tailored to the expected singularity behaviors. In $d=4$ and 5 dimensions we confirm that the critical behavior is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d=4$ are confirmed, and our results for the critical behavior of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation, and random fixed points. We estimate the critical exponent of the susceptibility to be $\ensuremath{\gamma}=1.305(5)$ at the random fixed point.In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the susceptibility and the free energy are obtained for the quenched bond-diluted Ising model in $d=3--5$ dimensions. They are analyzed using different extrapolation methods tailored to the expected singularity behaviors. In $d=4$ and 5 dimensions we confirm that the critical behavior is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d=4$ are confirmed, and our results for the critical behavior of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation, and random fixed points. We estimate the critical exponent of the susceptibility to be $\ensuremath{\gamma}=1.305(5)$ at the random fixed point.

arXiv:cond-mat/0606320Physical Review BOct 12, 200613 citations

{J}_{1}

and

{J}_{2}

. By studying a wide range of coupling ratios

{J}_{2}/{J}_{1}

we obtain compelling evidence for a critical behavior of the form $\ensuremath{\chi}\ensuremath{\sim}{t}^{\ensuremath{-}7/4}|\mathrm{ln}t{|}^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig.

d=3--5

dimensions. They are analyzed using different extrapolation methods tailored to the expected singularity behaviors. In

d=4

and 5 dimensions we confirm that the critical behavior is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in

d=4

are confirmed, and our results for the critical behavior of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation, and random fixed points. We estimate the critical exponent of the susceptibility to be $\ensuremath{\gamma}=1.305(5)$ at the random fixed point.