10,854 research outputs found
Magnetic phases in the S=1 Shastry-Sutherland model with uniaxial anisotropy
We explore the field induced magnetic phases of an model with
single-ion anisotropy and large Ising-like anisotropy on a Shastry Sutherland
lattice over a wide range of Hamiltonian parameters and applied magnetic field.
The multitude of ground state phases are characterized in detail in terms of
their thermodynamic properties and the underlying classical (Ising limit) spin
arrangements for the plateau phases are identified by calculating the static
structure factors. The enlarged local Hilbert space of the spins results
in several new ground state phases that are not realized for spins.
These include the quantum paramagnetic state that is ubiquitous to spins
with single ion anisotropy, two different spin supersolid phases (with distinct
longitudinal ordering) and a magnetization plateau that arises as a direct
descendant of the 1/3 plateau due to quantum fluctuations that are not possible
for spins. We predict the same mechanism will lead to plateaus at
smaller fractions of 1/3 for higher spins. The full momentum dependence of the
longitudinal and transverse components of the static structure factor is
calculated in the spin supersolid phase to demonstrate the simultaneous
existence of diagonal and off-diagonal long-range order as well as the
different longitudinal orderings.Comment: 7 pages, 7 figure
Evolutionary multiplayer games on graphs with edge diversity
Evolutionary game dynamics in structured populations has been extensively
explored in past decades. However, most previous studies assume that payoffs of
individuals are fully determined by the strategic behaviors of interacting
parties and social ties between them only serve as the indicator of the
existence of interactions. This assumption neglects important information
carried by inter-personal social ties such as genetic similarity, geographic
proximity, and social closeness, which may crucially affect the outcome of
interactions. To model these situations, we present a framework of evolutionary
multiplayer games on graphs with edge diversity, where different types of edges
describe diverse social ties. Strategic behaviors together with social ties
determine the resulting payoffs of interactants. Under weak selection, we
provide a general formula to predict the success of one behavior over the
other. We apply this formula to various examples which cannot be dealt with
using previous models, including the division of labor and relationship- or
edge-dependent games. We find that labor division facilitates collective
cooperation by decomposing a many-player game into several games of smaller
sizes. The evolutionary process based on relationship-dependent games can be
approximated by interactions under a transformed and unified game. Our work
stresses the importance of social ties and provides effective methods to reduce
the calculating complexity in analyzing the evolution of realistic systems.Comment: 50 pages, 7 figure
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