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| 2. |
- Baek, Seung Ki, 1979-, et al.
(författare)
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Curvature-induced frustration in the XY model on hyperbolic surfaces
- 2009
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Ingår i: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755. ; 79:6, s. 060106(R)-
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Tidskriftsartikel (refereegranskat)abstract
- We study low-temperature properties of the XY spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters scattered over the system. Asymptotic behavior of the spin-glass susceptibility suggests a zero-temperature glass transition, which is attributed to multiple optimal configurations of spin clusters due to nonzero surface curvature of the system. It implies that a constant ferromagnetic spin interaction on a regular lattice can exhibit glasslike behavior without possessing any disorder if the lattice is put on top of a negatively curved space such as a hyperbolic surface.
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| 3. |
- Baek, Seung Ki, 1979-, et al.
(författare)
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Flow improvement caused by agents who ignore traffic rules
- 2009
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Ingår i: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755. ; 80:1, s. 016111-
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Tidskriftsartikel (refereegranskat)abstract
- A system of agents moving along a road in both directions is studied numerically within a cellular-automata formulation. An agent steps to the right with probability q or to the left with 1-q when encountering other agents. Our model is restricted to two agent types, traffic-rule abiders (q=1) and traffic-rule ignorers (q=1/2), and the traffic flow, resulting from the interaction between these two types of agents, which is obtained as a function of density and relative fraction. The risk for jamming at a fixed density, when starting from a disordered situation, is smaller when every agent abides by a traffic rule than when all agents ignore the rule. Nevertheless, the absolute minimum occurs when a small fraction of ignorers are present within a majority of abiders. The characteristic features for the spatial structure of the flow pattern are obtained and discussed.
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| 4. |
- Baek, Seung Ki, et al.
(författare)
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Percolation in hyperbolic lattices
- 2009
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1063-651X .- 1095-3787. ; 79:1, s. 011124-011130
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Tidskriftsartikel (refereegranskat)abstract
- The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.
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| 5. |
- Baek, Seung Ki, et al.
(författare)
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True and quasi long-range order in the generalized q-state clock model
- 2009
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 80, s. 060101-
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Tidskriftsartikel (refereegranskat)abstract
- From consideration of the order-parameter distribution,we propose an observable which makes a clear distinction betweentrue and quasi long-range orders in the two-dimensionalgeneralized $q$-state clock model.Measuring this quantity by Monte Carlo simulations for $q=8$, weconstruct a phase diagram and identify critical properties acrossthe phase-separation lines among the true long-range order, quasilong-range order, and disorder. Our result supports the theoreticalprediction that there appears a discontinuous order-disorder transition assoon as the two phase-separation lines merge.
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| 6. |
- Seung Ki, Baek, 1979-, et al.
(författare)
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Phase transition of q-state clock models on heptagonal lattices
- 2009
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Ingår i: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755. ; 80:1, s. 011133-
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Tidskriftsartikel (refereegranskat)abstract
- We study the q-state clock models on heptagonal lattices assigned on a negatively curved surface. We show that the system exhibits three classes of equilibrium phases; in between ordered and disordered phases, an intermediate phase characterized by a diverging susceptibility with no magnetic order is observed at every q >= 2. The persistence of the third phase for all q is in contrast with the disappearance of the counterpart phase in a planar system for small q, which indicates the significance of nonvanishing surface-volume ratio that is peculiar in the heptagonal lattice. Analytic arguments based on Ginzburg-Landau theory and generalized Cayley trees make clear that the two-stage transition in the present system is attributed to an energy gap of spin-wave excitations and strong boundary-spin contributions. We further demonstrate that boundary effects break the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.
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