Energy gap of the bimodal two-dimensional Ising spin glass
@article{Atisattapong2008EnergyGO, title={Energy gap of the bimodal two-dimensional Ising spin glass}, author={Wanyok Atisattapong and J. F. Poulter}, journal={New Journal of Physics}, year={2008}, volume={10}, pages={093012} }
An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a distribution that is neither normal nor lognormal. Nevertheless, it is possible to estimate the most likely value and this is found to scale as L3T-2 exp (−4J/kT), for a L×L lattice. Our analysis also explains, for the first time, why a correlation length ξ~exp…
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References
SHOWING 1-10 OF 44 REFERENCES
Critical thermodynamics of the two-dimensional +/-J Ising spin glass.
- PhysicsPhysical review letters
- 2004
The exact partition function of 2d Ising spin glasses with binary couplings is computed, finding that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length scale grows as exp( J/T).
Nontrivial critical behavior of the free energy in the two-dimensional Ising spin glass with bimodal interactions
- Physics
- 2005
A detailed analysis of Monte Carlo data on the two-dimensional Ising spin glass with bimodal interactions shows that the free energy of the model has a nontrivial scaling. In particular, we show by…
Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
- Physics
- 2007
Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific…
Spin glass with non-random interactions
- Physics
- 1977
Magnetic systems with competing ferromagnetic and antiferromagnetic inter- actions are investigated and a few exact results are obtained. The possibility of exact solutions comes from the fact that…
Worm algorithm for two-dimensional spin glasses.
- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005
It is shown that the worm algorithm is efficient, particularly if free boundary conditions are used and accurate low-temperature specific heat data is obtained consistent with a form c approximately T-2 exp [-2J/( kB T) ].
Strong universality and algebraic scaling in two-dimensional Ising spin glasses.
- PhysicsPhysical review letters
- 2006
The scaling at low but nonzero temperatures is considered and numerical evidence that eta approximately equal 0 and nu approximately equal 3.5 in all cases suggests a unique universality class, suggesting a real space renormalization group approach.
The critical temperature of the two-dimensional ?J Ising spin glass
- Physics
- 2003
We have studied the two-dimensional ±J Ising model on the square lattice with a view to determine whether a spin glass can exist at small finite temperatures. By mapping the Ising model onto an…
Subextensive Singularity in the 2D ± J Ising Spin Glass
- Physics
- 2007
The statistics of low energy states of the 2D Ising spin glass with +1 and −1 bonds are studied for L × L square lattices with L≤ 48, and p = 0.5, where p is the fraction of negative bonds, using…
Exact integer algorithm for the two-dimensional +/-J Ising spin glass.
- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1993
An exact integer algorithm to compute the partition function of a two-dimensional ±J Ising spin glass given a set of quenched random bonds is described and the density of states is returned as a function of energy.