9,863 research outputs found
Two-Loop Crossover Scaling Functions of the O(N) Model
Using Environmentally Friendly Renormalization, we present an analytic
calculation of the series for the renormalization constants that describe the
equation of state for the model in the whole critical region. The
solution of the beta-function equation, for the running coupling to order two
loops, exhibits crossover between the strong coupling fixed point, associated
with the Goldstone modes, and the Wilson-Fisher fixed point. The Wilson
functions , and , and thus the
effective critical exponents associated with renormalization of the transverse
vertex functions, also exhibit non-trivial crossover between these fixed
points.Comment: 21 pages, 4 figures, version to appears in IJMPL
Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group
We study \l\f^4 theory using an environmentally friendly finite-temperature
renormalization group. We derive flow equations, using a fiducial temperature
as flow parameter, develop them perturbatively in an expansion free from
ultraviolet and infrared divergences, then integrate them numerically from zero
to temperatures above the critical temperature. The critical temperature, at
which the mass vanishes, is obtained by integrating the flow equations and is
determined as a function of the zero-temperature mass and coupling. We
calculate the field expectation value and minimum of the effective potential as
functions of temperature and derive some universal amplitude ratios which
connect the broken and symmetric phases of the theory. The latter are found to
be in good agreement with those of the three-dimensional Ising model obtained
from high- and low-temperature series expansions.Comment: 14 pages of LaTeX. Postscript figures available upon request form
[email protected]
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The Adjudication and Enforcement of Rights After Brexit
This report records the inaugural meeting and roundtable of the Brexit and Rights Engagement Network (BREN) on Tuesday 3rd July 2018 at Edinburgh Law School. Attendees at the roundtable included network members, fellow academics, representatives of the Scottish Parliament, the Scottish Government, the Scottish Human Rights Commission, the Equality and Human Rights Commission, the legal professions, and NGOs. Two years after the EU Referendum and only a few days after the European Union (Withdrawal) Act 2018 (the 2018 Act) receiving Royal Assent, the Brexit and Rights Engagement Network met for the first time. The purpose of the roundtable was to ignite debate amongst legal scholars and policy makers, and others working in a rights environment relating to interpretation, adjudication and enforcement of rights in the lead up to, and following “Brexit Day,” (March 29, 2019). This report is split into two sections, Part A will consider the adjudication of EU rights, but also their enforcement under the 2018 Act and the Withdrawal Agreement, whilst ‘options for the future’ will be broached in Part B
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Estimating drizzle drop size and precipitation rate using two-colour lidar measurements
A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution.
The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions
The Specific Heat of a Ferromagnetic Film.
We analyze the specific heat for the vector model on a -dimensional
film geometry of thickness using ``environmentally friendly''
renormalization. We consider periodic, Dirichlet and antiperiodic boundary
conditions, deriving expressions for the specific heat and an effective
specific heat exponent, \alpha\ef. In the case of , for , by
matching to the exact exponent of the two dimensional Ising model we capture
the crossover for \xi_L\ra\infty between power law behaviour in the limit
{L\over\xi_L}\ra\infty and logarithmic behaviour in the limit
{L\over\xi_L}\ra0 for fixed , where is the correlation length in
the transverse dimensions.Comment: 21 pages of Plain TeX. Postscript figures available upon request from
[email protected]
Topological Phase Transitions and Holonomies in the Dimer Model
We demonstrate that the classical dimer model defined on a toroidal hexagonal
lattice acquires holonomy phases in the thermodynamic limit. When all
activities are equal the lattice sizes must be considered mod 6 in which case
the finite size corrections to the bulk partition function correspond to a
massless Dirac Fermion in the presence of a flat connection with nontrivial
holonomy. For general bond activities we find that the phase transition in this
model is a topological one, where the torus degenerates and its modular
parameter becomes real at the critical temperature. We argue that these
features are generic to bipartite dimer models and we present a more general
lattice whose continuum partition function is that of a massive Dirac Fermion.Comment: 7 pages, 4 figures. Minor corrections with additional figure
An Analytic Equation of State for Ising-like Models
Using an Environmentally Friendly Renormalization we derive, from an
underlying field theory representation, a formal expression for the equation of
state, , that exhibits all desired asymptotic and analyticity
properties in the three limits , and . The only
necessary inputs are the Wilson functions , and
, associated with a renormalization of the transverse vertex
functions. These Wilson functions exhibit a crossover between the Wilson-Fisher
fixed point and the fixed point that controls the coexistence curve.
Restricting to the case N=1, we derive a one-loop equation of state for naturally parameterized by a ratio of non-linear scaling fields. For
we show that a non-parameterized analytic form can be deduced. Various
asymptotic amplitudes are calculated directly from the equation of state in all
three asymptotic limits of interest and comparison made with known results. By
positing a scaling form for the equation of state inspired by the one-loop
result, but adjusted to fit the known values of the critical exponents, we
obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure
An Economic Evaluation of Irish Salmon Fishing General Summary of Results. ESRI Memorandum Series No. 99 1974
The purpose of the study was to investigate the economies of salmon fishing in Ireland. Essentially, it set out to answer the question "how valuable was the Irish salmon industry to the economy in 1970?" In order to answer this
question, the study tried to evaluate the economic impact of angling and commercial fishing on the various districts, determine the capacity of the industry for future development and provide information to assist in the more effective marketing of salmon and sea-trout angling. Although the survey was confined to 1970, its findings may be updated for subsequent years by means of the regularly published data on catches and numbers of licences, and by appropriate price indices
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