Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
| Autor: | Creighton K. Thomas, Helmut G. Katzgraber, Katharina Janzen |
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| Rok vydání: | 2012 |
| Předmět: |
Spin glass
Condensed matter physics Monte Carlo method FOS: Physical sciences Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Renormalization group Condensed Matter::Disordered Systems and Neural Networks Universality (dynamical systems) Exponent Antiferromagnetism Condensed Matter::Strongly Correlated Electrons Statistical physics Boolean data type Mathematics Phase diagram |
| DOI: | 10.48550/arxiv.1202.1153 |
| Popis: | We study the critical behavior of Boolean variables on scale-free networks with competing interactions (Ising spin glasses). Our analytical results for the disorder-network-decay-exponent phase diagram are verified using Monte Carlo simulations. When the probability of positive (ferromagnetic) and negative (antiferromagnetic) interactions is the same, the system undergoes a finite-temperature spin-glass transition if the exponent that describes the decay of the interaction degree in the scale-free graph is strictly larger than 3. However, when the exponent is equal to or less than 3, a spin-glass phase is stable for all temperatures. The robustness of both the ferromagnetic and spin-glass phases suggests that Boolean decision problems on scale-free networks are quite stable to local perturbations. Finally, we show that for a given decay exponent spin glasses on scale-free networks seem to obey universality. Furthermore, when the decay exponent of the interaction degree is larger than 4 in the spin-glass sector, the universality class is the same as for the mean-field Sherrington-Kirkpatrick Ising spin glass. Comment: 14 pages, lots of figures and 2 tables |
| Databáze: | OpenAIRE |
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