Relationship between the structure of the ground level and frustration in ±J Ising lattices

Valdés, J.F.; Cartes, J.; Vogel, E.E.; Kobe, S.; Klotz, Tilla

doi:10.1016/s0378-4371(98)00192-7

Cited by 15 publications

(8 citation statements)

References 5 publications

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“…Also transfer-matrix techniques have been applied [39] for 43 spin glasses. To evaluate all ground states, similar algorithms have been applied to two-dimensional systems as well [40,41,42,43,44,45]. A more sophisticated method called Branch-and-Cut [46, 471 works by rewriting the quadratic energy function as a linear function with an additional set of inequalities which must hold for the feasible solutions.…”

Section: Genetic Cluster-exact Approximationmentioning

confidence: 99%

Optimization Algorithms in Physics

Hartmann¹,

Rieger²

2001

248

297

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PrefaceThis book is an interdisciplinary book: it tries to teach physicists the basic knowledge of combinatorial and stochastic optimization and describes to the computer scientists physical problems and theoretical models in which their optimization algorithms are needed. It is a unique book since it describes theoretical models and practical situation in physics in which optimization problems occur, and it explains from a physicists point of view the sophisticated and highly efficient algorithmic techniques that otherwise can only be found specialized computer science textbooks or even just in research journals. Traditionally, there has always been a strong scientific interaction between physicists and mathematicians in developing physics theories. However, even though numerical computations are now commonplace in physics, no comparable interaction between physicists and computer scientists has been developed. Over the last three decades the design and the analysis of algorithms for decision and optimization problems have evolved rapidly. Most of the active transfer of the results was to economics and engineering and many algorithmic developments were motivated by applications in these areas. The few interactions between physicists and computer scientists were often successful and provided new insights in both fields. For example, in one direction, the algorithmic community has profited from the introduction of general purpose optimization tools like the simulated annealing technique that originated in the physics community. In the opposite direction, algorithms in linear, nonlinear, and discrete optimization sometimes have the potential to be useful tools in physics, in particular in the study of strongly disordered, amorphous and glassy materials. These systems have in common a highly non-trivial minimal energy configuration, whose characteristic features dominate the physics a t low temperatures. For a theoretical understanding the knowledge of the so called "ground states" of model Hamiltonians, or optimal solutions of appropriate cost functions, is mandatory. To this end an efficient algorithm, applicable to reasonably sized instances, is a necessary condition. The list of interesting physical problems in this context is long, it ranges from disordered magnets, structural glasses and superconductors through polymers, membranes, and proteins to neural networks. The predominant method used by physicists to study these questions numerically are Monte Carlo simulations and/or simulated annealing. These methods are doomed to fail in the most interesting situations. But, as pointed out above, many useful results in optimization algorithms research never reach the physics community, and interesting computational problems in physics do not come to the attention of algorithm designers. We therefore think that there is a definite need VI Preface to intensify the interaction between the computer science and physics communities. We hope that this book will help to extend the bridge between these two groups. Since one...

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Section: Genetic Cluster-exact Approximationmentioning

confidence: 99%

Optimization Algorithms in Physics

Hartmann¹,

Rieger²

2001

248

297

View full text Add to dashboard Cite

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“…Calculations begin recognizing all of the CSS of each sample belonging to a set of 2000 randomly generated samples of each size. This process is closely related to finding the so-called "diluted lattice" that prevails after removing all frustrated bonds [19], so the algorithms designed for that purpose can also be used here. Let us first pick any arbitrary ground state configuration denoted by an asterisk ( * ) fixing one of the two possible relative orientations of the CSS, thus becoming a reference configuration.…”

Section: Model and Basic Definitionsmentioning

confidence: 99%

Novel order parameter to describe the critical behavior of Ising spin glass models

Romá

Nieto

Ramírez-Pastor

et al. 2006

Physica A: Statistical Mechanics and its Applications

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A novel order parameter Φ for spin glasses is defined based on topological criteria and with a clear physical interpretation. Φ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson ±J model on a square lattice, comparing its properties with the usual q order parameter. Finite size scaling procedures are performed. Results and analyses based on Φ confirm a zero temperature phase transition and allow to identify the low temperature phase. The advantages of Φ are brought out and its physical meaning is established.

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“…Not all interactions can be satisfied even for a ground state, so energies are usually higher than À 3N, which would be the case for a fully unfrustrated system like the pure F case (x¼0.0). The degeneracy of the ground manifold is usually very large and it is formed by clusters of states separated by energy barriers [11,12]. To simplify notation, energies will be expressed in units of J.…”

Section: Review Of Main Definitionsmentioning

confidence: 99%