Periodic boundary conditions on the pseudosphere

Sausset, François; Tarjus, Gilles

doi:10.1088/1751-8113/40/43/004

Cited by 63 publications

(78 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the two-dimensional manifold Σ is a compact Riemann 2-surface of genus g ≥ 2. Further details on this kind of compactification scheme can be found in [17,18]. The configuration (2.2) is an asymptotically locally AdS spacetime.…”

Section: Mode Analysis Of the Wave Equation Of A Scalar Field In The mentioning

confidence: 99%

Hawking radiation via gravitational anomalies in nonspherical topologies

Papantonopoulos

Skamagoulis

2009

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

Section: Mode Analysis Of the Wave Equation Of A Scalar Field In The mentioning

confidence: 99%

Hawking radiation via gravitational anomalies in nonspherical topologies

Papantonopoulos

Skamagoulis

2009

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…Since it was pointed out that a system may have a novel behavior due to the presence of a nonvanishing boundary [7], there have been ongoing studies to clarify this issue [4,6,[8][9][10][11]. While the boundary effects can be sometimes excluded, for example, by using a periodic boundary condition [12] or by mathematical abstractions [5,[13][14][15], it is often crucial to understand how a boundary affects the physical properties since it may give the most important contribution to an observed behavior as will be explained in this work.…”

Section: Introductionmentioning

confidence: 99%

Phase transition ofq-state clock models on heptagonal lattices

et al. 2009

View full text Add to dashboard Cite

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 breaks the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.

show abstract

“…As a consequence of the latter property, studying finite-size effects at constant curvature requires to change the boundary condition. Building on our earlier work [15], we have implemented two different pbc's: an octagonal pbc ( Fig. 1(a)) and a pbc with a larger unit cell formed by a regular 14-gon with a specific pairing of the edges.…”

mentioning

confidence: 99%

Tuning the Fragility of a Glass-Forming Liquid by Curving Space

2008

View full text Add to dashboard Cite

We investigate the influence of space curvature, and of the associated "frustration", on the dynamics of a model glassformer: a monatomic liquid on the hyperbolic plane. We find that the system's fragility, i.e. the sensitivity of the relaxation time to temperature changes, increases as one decreases the frustration. As a result, curving space provides a way to tune fragility and make it as large as wanted. We also show that the nature of the emerging "dynamic heterogeneities", another distinctive feature of slowly relaxing systems, is directly connected to the presence of frustration-induced topological defects.Among the many anomalous properties associated with glass formation, "fragility" is one that has attracted much attention [1,2,3,4,5,6,7]. Large fragility, i.e. large deviation of the temperature dependence of the viscosity and of the structural relaxation time from an Arrhenius behavior, is usually taken as the signature of a collective phenomenon that grows as temperature decreases. This is certainly one incentive for the continuing search for a theory of the glass transition [2,4,5,6,7]. Yet, the absence of a simple glassforming liquid model in which one can control the degree of fragility, hence the extent to which collective behavior develops, has hindered progress on developing and testing candidate theories.Since the early work of Frank[8], a promising line of research on supercooled liquids and the glass transition has relied on the concept of "geometric frustration" [7,9,10]. Frustration in this context can be defined as an incompatibility between extension of the local order preferred in a liquid and tiling of the whole space. The paradigm is the icosahedral order in metallic liquids and glasses, which although locally favored cannot tile space due to topological reasons [8]. Frustration of the icosahedral order, however, can be suppressed by leaving the Euclidean world and curving space [9,10]. In a series of insightful articles [10,11,12], Nelson and collaborators have proposed a simpler two-dimensional (2D) analog: by placing a liquid of disks on a 2D manifold of constant negative curvature (the hyperbolic plane), the local hexagonal order that can tile the ordinary Euclidean plane is now frustrated in a way which mimics by many aspects the frustration of icosahedral order in 3D Euclidean space. The model of a monatomic liquid on the hyperbolic plane therefore offers the opportunity to investigate, at a microscopic level, the influence of the degree of frustration, here controlled by the curvature, on the slowing down of the relaxation associated with glass formation.We present the results of the first computer simulation of the dynamics of a liquid in curved hyperbolic space. The hyperbolic plane H 2 , also called pseudosphere or Bolyai-Lobatchevski plane, is a Riemannian surface of constant negative curvature [13,14]. Contrary to a sphere, which is a surface of constant positive curvature, H 2 is infinite: this allows one to envisage the thermodynamic limit at constant curvature. However, ...

show abstract

Periodic boundary conditions on the pseudosphere

Cited by 63 publications

References 58 publications

Hawking radiation via gravitational anomalies in nonspherical topologies

Hawking radiation via gravitational anomalies in nonspherical topologies

Phase transition ofq-state clock models on heptagonal lattices

Tuning the Fragility of a Glass-Forming Liquid by Curving Space

Contact Info

Product

Resources

About