6,595 research outputs found
25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
25th-order high-temperature series are computed for a general
nearest-neighbor three-dimensional Ising model with arbitrary potential on the
simple cubic lattice. In particular, we consider three improved potentials
characterized by suppressed leading scaling corrections. Critical exponents are
extracted from high-temperature series specialized to improved potentials,
obtaining , , ,
, , . Moreover, biased
analyses of the 25th-order series of the standard Ising model provide the
estimate for the exponent associated with the leading scaling
corrections. By the same technique, we study the small-magnetization expansion
of the Helmholtz free energy. The results are then applied to the construction
of parametric representations of the critical equation of state, using a
systematic approach based on a global stationarity condition. Accurate
estimates of several universal amplitude ratios are also presented.Comment: 40 pages, 15 figure
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
Videoconference-based creativity workshops for mental health staff during the COVID-19 pandemic
Background
COVID-19 presented significant challenges to psychiatric staff, while social distancing and remote working necessitated digital communications. NHS England prioritised staff wellbeing. Arts-based creativity interventions appear to improve psychological wellbeing, so this study evaluated online Creativity Workshops as a staff support response for COVID-19-related stress.
Methods
Participants were staff from a South London NHS psychiatric hospital. Group Creativity Workshops were facilitated via Microsoft Teams. Acceptability data on pre- and post-workshop mood and attitudes were self-reported by participants. Feasibility data were gathered from adherence to number of workshop components delivered.
Results
Eight workshops were delivered in May-September 2020 (N = 55) with high adherence to components. Participants reported significantly increased positive mood and attitudes towards themselves and others; and decreased stress and anxiety.
Conclusions
Online Creativity Workshops appear feasible and acceptable in reducing stress in psychiatric staff. Integrating a programme of Creativity Workshops within healthcare staff support may benefit staff wellbeing
Analytic Inversion of Emission Lines of Arbitrary Optical Depth for the Structure of Supernova Ejecta
We derive a method for inverting emission line profiles formed in supernova
ejecta. The derivation assumes spherical symmetry and homologous expansion
(i.e., ), is analytic, and even takes account of occultation by
a pseudo-photosphere. Previous inversion methods have been developed which are
restricted to optically thin lines, but the particular case of homologous
expansion permits an analytic result for lines of {\it arbitrary} optical
depth. In fact, we show that the quantity that is generically retrieved is the
run of line intensity with radius in the ejecta. This result is
quite general, and so could be applied to resonance lines, recombination lines,
etc. As a specific example, we show how to derive the run of (Sobolev) optical
depth with radius in the case of a pure resonance scattering
emission line.Comment: 6 pages, no figures, to appear in Astrophysical Journal Letters,
requires aaspp4.sty to late
Rapid Suppression of the Spin Gap in Zn-doped CuGeO_3 and SrCu_2O_3
The influence of non-magnetic impurities on the spectrum and dynamical spin
structure factor of a model for CuGeO is studied. A simple extension to
Zn-doped is also discussed. Using Exact Diagonalization
techniques and intuitive arguments we show that Zn-doping introduces states in
the Spin-Peierls gap of CuGeO. This effect can beunderstood easily in the
large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins,
which interact with each other through very weak effective antiferromagnetic
couplings. When the dimerization is small, a similar effect is observed but now
with the free S=1/2 spins being the resulting S=1/2 ground state of severed
chains with an odd number of sites. Experimental consequences of these results
are discussed. It is interesting to observe that the spin correlations along
the chains are enhanced by Zn-doping according to the numerical data presented
here. As recent numerical calculations have shown, similar arguments apply to
ladders with non-magnetic impurities simply replacing the tendency to
dimerization in CuGeO by the tendency to form spin-singlets along the rungs
in SrCuO.Comment: 7 pages, 8 postscript figures, revtex, addition of figure 8 and a
section with experimental predictions, submmited to Phys. Rev. B in May 199
Extension to order of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
Using a renormalized linked-cluster-expansion method, we have extended to
order the high-temperature series for the susceptibility
and the second-moment correlation length of the spin-1/2 Ising models on
the sc and the bcc lattices. A study of these expansions yields updated direct
estimates of universal parameters, such as exponents and amplitude ratios,
which characterize the critical behavior of and . Our best
estimates for the inverse critical temperatures are
and . For the
susceptibility exponent we get and for the correlation
length exponent we get .
The ratio of the critical amplitudes of above and below the critical
temperature is estimated to be . The analogous ratio for
is estimated to be . For the correction-to-scaling
amplitude ratio we obtain .Comment: Misprints corrected, 8 pages, latex, no figure
Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
High-temperature series are computed for a generalized Ising model with
arbitrary potential. Two specific ``improved'' potentials (suppressing leading
scaling corrections) are selected by Monte Carlo computation. Critical
exponents are extracted from high-temperature series specialized to improved
potentials, achieving high accuracy; our best estimates are:
, , , ,
. By the same technique, the coefficients of the small-field
expansion for the effective potential (Helmholtz free energy) are computed.
These results are applied to the construction of parametric representations of
the critical equation of state. A systematic approximation scheme, based on a
global stationarity condition, is introduced (the lowest-order approximation
reproduces the linear parametric model). This scheme is used for an accurate
determination of universal ratios of amplitudes. A comparison with other
theoretical and experimental determinations of universal quantities is
presented.Comment: 65 pages, 1 figure, revtex. New Monte Carlo data by Hasenbusch
enabled us to improve the determination of the critical exponents and of the
equation of state. The discussion of several topics was improved and the
bibliography was update
Critical behavior of the three-dimensional XY universality class
We improve the theoretical estimates of the critical exponents for the
three-dimensional XY universality class. We find alpha=-0.0146(8),
gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and
delta=4.780(2). We observe a discrepancy with the most recent experimental
estimate of alpha; this discrepancy calls for further theoretical and
experimental investigations. Our results are obtained by combining Monte Carlo
simulations based on finite-size scaling methods, and high-temperature
expansions. Two improved models (with suppressed leading scaling corrections)
are selected by Monte Carlo computation. The critical exponents are computed
from high-temperature expansions specialized to these improved models. By the
same technique we determine the coefficients of the small-magnetization
expansion of the equation of state. This expansion is extended analytically by
means of approximate parametric representations, obtaining the equation of
state in the whole critical region. We also determine the specific-heat
amplitude ratio.Comment: 61 pages, 3 figures, RevTe
Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices
For the classical N-vector model, with arbitrary N, we have computed through
order \beta^{17} the high temperature expansions of the second field derivative
of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body
centered cubic lattices. (The N-vector model is also known as the O(N)
symmetric classical spin Heisenberg model or, in quantum field theory, as the
lattice
O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on
the two lattices, and by carefully allowing for the corrections to scaling, we
obtain updated estimates of the critical parameters and more accurate tests of
the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of
values of the spin dimensionality N, including
N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model],
N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently
extended series for the susceptibility and for the second correlation moment,
we also compute the dimensionless renormalized four point coupling constants
and some universal ratios of scaling correction amplitudes in fair agreement
with recent renormalization group estimates.Comment: 23 pages, latex, no figure
Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
We consider the problem of `discrete-time persistence', which deals with the
zero-crossings of a continuous stochastic process, X(T), measured at discrete
times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no
crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n,
where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D,
is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval
Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta
T) and conclude that experimental measurements of persistence for smooth
processes, such as diffusion, are less sensitive to the effects of discrete
sampling than measurements of a randomly accelerated particle or random walker.
We extend the matrix method developed by us previously [Phys. Rev. E 64,
015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and
the one-dimensional random acceleration problem. We also consider `alternating
persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure
- …