Groundstate threshold pc in Ising frustration systems on 2D regular lattices

Bendisch, J.

doi:10.1016/0378-4371(94)90166-x

Cited by 14 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further, note that p c and ν found here agree well with the values p c = 0.1583 (6) and ν = 1.47(9) that characterize the negativeweight percolation of loops on 2d lattice graphs with a honeycomb geometry and fully periodic boundary conditions [13]. Finally, the location of the critical point obtained here via FSS analysis is close to the theoretical prediction p c,tr = 0.15, that was obtained for systems with fully periodic boundary conditions using the adjoined problem approach [24,16].…”

Section: Discussionsupporting

confidence: 89%

A dedicated algorithm for calculating ground states for the triangular random bond Ising model

Melchert

Hartmann

2011

Computer Physics Communications

View full text Add to dashboard Cite

In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state problem can be mapped to an auxiliary minimum-weight perfect matching problem, solvable in polynomial time. Consequently, the ground state properties as well as minimumenergy domain wall (MEDW) excitations for very large 2d systems, e.g. lattice graphs with up to N = 384 × 384 spins, can be analyzed very fast. Here, we investigate the critical behavior of the corresponding T = 0 ferromagnet to spin-glass transition, signaled by a breakdown of the magnetization, using finite-size scaling analyses of the magnetization and MEDW excitation energy and we contrast our numerical results with previous simulations and presumably exact results.

show abstract

Section: Discussionsupporting

confidence: 89%

A dedicated algorithm for calculating ground states for the triangular random bond Ising model

Melchert

Hartmann

2011

Computer Physics Communications

View full text Add to dashboard Cite

show abstract

“…If one is interested in obtaining the partition sum, without obtaining spin configurations, one can also treat systems with full periodic boundary conditions in polynomial time, by using transfer-matrix approaches 24,25,26,27 , but the running time is again strongly increasing, limiting the investigations to small systems. The most recent studies are based on matching algorithms 29,30,31,32,33,34,35,36,37 , while other exact approaches can be found in Refs. 38,39,40 .…”

Section: Algorithmmentioning

confidence: 99%

Generating droplets in two-dimensional Ising spin glasses using matching algorithms

Hartmann¹,

Moore²

2004

Phys. Rev. B

View full text Add to dashboard Cite

We study the behavior of droplets for two-dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross, and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.

show abstract

“…For all toroidal interaction graphs, provided interactions have v alue J and there is no eld, Barahona found a polynomial time algorithm 2]. But for practical purposes this algorithm is not useful since the running time is proportional to jV j 7 . In the Gaussian model with zero eld, no polynomial time algorithm is known, and it is not clear if there exists one.…”

Section: Ground States and Maximum Cutsmentioning

confidence: 99%

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

et al. 1995

View full text Add to dashboard Cite

In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic eld. We s h o w h o w using a technique called branch and cut, the exact ground states of grids of sizes up to 100 100 can be determined in a moderate amount of computation time, and we r e p o r t on extensive computational tests. With our method we produce results based on more than 20 000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like M o n te Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero eld is ;1:317.

show abstract

Groundstate threshold pc in Ising frustration systems on 2D regular lattices

Cited by 14 publications

References 11 publications

A dedicated algorithm for calculating ground states for the triangular random bond Ising model

A dedicated algorithm for calculating ground states for the triangular random bond Ising model

Generating droplets in two-dimensional Ising spin glasses using matching algorithms

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

Contact Info

Product

Resources

About