294 research outputs found
Equilibrium valleys in spin glasses at low temperature
We investigate the 3-dimensional Edwards-Anderson spin glass model at low
temperature on simple cubic lattices of sizes up to L=12. Our findings show a
strong continuity among T>0 physical features and those found previously at
T=0, leading to a scenario with emerging mean field like characteristics that
are enhanced in the large volume limit. For instance, the picture of space
filling sponges seems to survive in the large volume limit at T>0, while
entropic effects play a crucial role in determining the free-energy degeneracy
of our finite volume states. All of our analysis is applied to equilibrium
configurations obtained by a parallel tempering on 512 different disorder
realizations. First, we consider the spatial properties of the sites where
pairs of independent spin configurations differ and we introduce a modified
spin overlap distribution which exhibits a non-trivial limit for large L.
Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations
into valleys. On average these valleys have free-energy differences of O(1),
but a difference in the (extensive) internal energy that grows significantly
with L; there is thus a large interplay between energy and entropy
fluctuations. We also find that valleys typically differ by sponge-like space
filling clusters, just as found previously for low-energy system-size
excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional
reference
Attractive instability of oppositely charged membranes induced by charge density fluctuations
We predict the conditions under which two oppositely charged membranes show a
dynamic, attractive instability. Two layers with unequal charges of opposite
sign can repel or be stable when in close proximity. However, dynamic charge
density fluctuations can induce an attractive instability and thus facilitate
fusion. We predict the dominant instability modes and timescales and show how
these are controlled by the relative charge and membrane viscosities. These
dynamic instabilities may be the precursors of membrane fusion in systems where
artificial vesicles are engulfed by biological cells of opposite charge
Discrete energy landscapes and replica symmetry breaking at zero temperature
The order parameter P(q) for disordered systems with degenerate ground-states
is reconsidered. We propose that entropy fluctuations lead to a trivial P(q) at
zero temperature as in the non-degenerate case, even if there are zero-energy
large-scale excitations (complex energy landscape). Such a situation should
arise in the 3-dimensional +-J Ising spin glass and in MAX-SAT. Also, we argue
that if the energy landscape is complex with a finite number of ground-state
families, then replica symmetry breaking reappears at positive temperature.Comment: 7 pages; clarifications on valley definition
Extension and approximation of -subharmonic functions
Let be a bounded domain, and let be a
real-valued function defined on the whole topological boundary . The aim of this paper is to find a characterization of the functions
which can be extended to the inside to a -subharmonic function under
suitable assumptions on . We shall do so by using a function algebraic
approach with focus on -subharmonic functions defined on compact sets. We
end this note with some remarks on approximation of -subharmonic functions
Assessing the applicability of public health intervention evaluations from one setting to another: a methodological study of the usability and usefulness of assessment tools and frameworks
BACKGROUND: Public health interventions can be complicated, complex and context dependent, making the assessment of applicability challenging. Nevertheless, for them to be of use beyond the original study setting, they need to be generalisable to other settings and, crucially, research users need to be able to identify to which contexts it may be applicable. There are many tools with set criteria for assessing generalisability/applicability, yet few seem to be widely used and there is no consensus on which should be used, or when. This methodological study aimed to test these tools to assess how easy they were to use and how useful they appeared to be. METHODS: We identified tools from an existing review and an update of its search. References were screened on pre-specified criteria. Included tools were tested by using them to assess the applicability of a Swedish weight management intervention to the English context. Researcher assessments and reflections on the usability and utility of the tools were gathered using a standard pro-forma. RESULTS: Eleven tools were included. Their length, content, style and time required to complete varied. No tool was considered ideal for assessing applicability. Their limitations included unrealistic criteria (requiring unavailable information), a focus on implementation to the neglect of transferability (i.e. little focus on potential effectiveness in the new setting), overly broad criteria (associated with low reliability), and a lack of an explicit focus on how interventions worked (i.e. their mechanisms of action). CONCLUSION: Tools presenting criteria ready to be used may not be the best method for applicability assessments. They are likely to be either too long or incomplete, too focused on differences and fail to address elements that matter for the specific topic of interest. It is time to progress from developing lists of set criteria that are not widely used in the literature, to creating a new approach to applicability assessment. Focusing on mechanisms of action, rather than solely on characteristics, could be a useful approach, and one that remains underutilised in current tools. New approaches to assessing generalisability that evolve away from checklist style assessments need to be developed, tested, reported and discussed
Discreteness and entropic fluctuations in GREM-like systems
Within generalized random energy models, we study the effects of energy
discreteness and of entropy extensivity in the low temperature phase. At zero
temperature, discreteness of the energy induces replica symmetry breaking, in
contrast to the continuous case where the ground state is unique. However, when
the ground state energy has an extensive entropy, the distribution of overlaps
P(q) instead tends towards a single delta function in the large volume limit.
Considering now the whole frozen phase, we find that P(q) varies continuously
with temperature, and that state-to-state fluctuations of entropy wash out the
differences between the discrete and continuous energy models.Comment: 7 pages, 3 figure, 2 figures are added, the volume changes from 4
pages to 7 page
State Hierarchy Induced by Correlated Spin Domains in short range spin glasses
We generate equilibrium configurations for the three and four dimensional
Ising spin glass with Gaussian distributed couplings at temperatures well below
the transition temperature T_c. These states are analyzed by a recently
proposed method using clustering. The analysis reveals a hierarchical state
space structure. At each level of the hierarchy states are labeled by the
orientations of a set of correlated macroscopic spin domains. Our picture of
the low temperature phase of short range spin glasses is that of a State
Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low
temperature phase is manifest in the fact that the composition of such a spin
domain (i.e. its constituent spins), as well as its identifying label, are
defined and determined by the ``location'' in the state hierarchy at which it
appears. Mapping out the phase space structure by means of the orientations
assumed by these domains enhances our ability to investigate the overlap
distribution, which we find to be non-trivial. Evidence is also presented that
these states may have a non-ultrametric structure.Comment: 30 pages, 17 figure
Pores in Bilayer Membranes of Amphiphilic Molecules: Coarse-Grained Molecular Dynamics Simulations Compared with Simple Mesoscopic Models
We investigate pores in fluid membranes by molecular dynamics simulations of
an amphiphile-solvent mixture, using a molecular coarse-grained model. The
amphiphilic membranes self-assemble into a lamellar stack of amphiphilic
bilayers separated by solvent layers. We focus on the particular case of
tension less membranes, in which pores spontaneously appear because of thermal
fluctuations. Their spatial distribution is similar to that of a random set of
repulsive hard discs. The size and shape distribution of individual pores can
be described satisfactorily by a simple mesoscopic model, which accounts only
for a pore independent core energy and a line tension penalty at the pore
edges. In particular, the pores are not circular: their shapes are fractal and
have the same characteristics as those of two dimensional ring polymers.
Finally, we study the size-fluctuation dynamics of the pores, and compare the
time evolution of their contour length to a random walk in a linear potential
Evidence for the double degeneracy of the ground-state in the 3D spin glass
A bivariate version of the multicanonical Monte Carlo method and its
application to the simulation of the three-dimensional Ising spin glass
are described. We found the autocorrelation time associated with this
particular multicanonical method was approximately proportional to the system
volume, which is a great improvement over previous methods applied to
spin-glass simulations. The principal advantage of this version of the
multicanonical method, however, was its ability to access information
predictive of low-temperature behavior. At low temperatures we found results on
the three-dimensional Ising spin glass consistent with a double
degeneracy of the ground-state: the order-parameter distribution function
converged to two delta-function peaks and the Binder parameter
approached unity as the system size was increased. With the same density of
states used to compute these properties at low temperature, we found their
behavior changing as the temperature is increased towards the spin glass
transition temperature. Just below this temperature, the behavior is consistent
with the standard mean-field picture that has an infinitely degenerate ground
state. Using the concept of zero-energy droplets, we also discuss the structure
of the ground-state degeneracy. The size distribution of the zero-energy
droplets was found to produce the two delta-function peaks of .Comment: 33 pages with 31 eps figures include
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