8,213 research outputs found
Environmentally Friendly Renormalization
We analyze the renormalization of systems whose effective degrees of freedom
are described in terms of fluctuations which are ``environment'' dependent.
Relevant environmental parameters considered are: temperature, system size,
boundary conditions, and external fields. The points in the space of \lq\lq
coupling constants'' at which such systems exhibit scale invariance coincide
only with the fixed points of a global renormalization group which is
necessarily environment dependent. Using such a renormalization group we give
formal expressions to two loops for effective critical exponents for a generic
crossover induced by a relevant mass scale . These effective exponents are
seen to obey scaling laws across the entire crossover, including hyperscaling,
but in terms of an effective dimensionality, d\ef=4-\gl, which represents the
effects of the leading irrelevant operator. We analyze the crossover of an
model on a dimensional layered geometry with periodic, antiperiodic
and Dirichlet boundary conditions. Explicit results to two loops for effective
exponents are obtained using a [2,1] Pad\'e resummed coupling, for: the
``Gaussian model'' (), spherical model (), Ising Model (),
polymers (), XY-model () and Heisenberg () models in four
dimensions. We also give two loop Pad\'e resummed results for a three
dimensional Ising ferromagnet in a transverse magnetic field and corresponding
one loop results for the two dimensional model. One loop results are also
presented for a three dimensional layered Ising model with Dirichlet and
antiperiodic boundary conditions. Asymptotically the effective exponents are in
excellent agreement with known results.Comment: 76 pages of Plain Tex, Postscript figures available upon request from
[email protected], preprint numbers THU-93/14, DIAS-STP-93-1
Geometry the Renormalization Group and Gravity
We discuss the relationship between geometry, the renormalization group (RG)
and gravity. We begin by reviewing our recent work on crossover problems in
field theory. By crossover we mean the interpolation between different
representations of the conformal group by the action of relevant operators. At
the level of the RG this crossover is manifest in the flow between different
fixed points induced by these operators. The description of such flows requires
a RG which is capable of interpolating between qualitatively different degrees
of freedom. Using the conceptual notion of course graining we construct some
simple examples of such a group introducing the concept of a ``floating'' fixed
point around which one constructs a perturbation theory. Our consideration of
crossovers indicates that one should consider classes of field theories,
described by a set of parameters, rather than focus on a particular one. The
space of parameters has a natural metric structure. We examine the geometry of
this space in some simple models and draw some analogies between this space,
superspace and minisuperspace.Comment: 16 pages of LaTex, DIAS-STP-92-3
Why Two Renormalization Groups are Better than One
The advantages of using more than one renormalization group (RG) in problems
with more than one important length scale are discussed. It is shown that: i)
using different RG's can lead to complementary information, i.e. what is very
difficult to calculate with an RG based on one flow parameter may be much more
accessible using another; ii) using more than one RG requires less physical
input in order to describe via RG methods the theory as a function of its
parameters; iii) using more than one RG allows one to solve problems with more
than one diverging length scale. The above points are illustrated concretely in
the context of both particle physics and statistical physics using the
techniques of environmentally friendly renormalization. Specifically, finite
temperature theory, an Ising-type system in a film geometry, an
Ising-type system in a transverse magnetic field, the QCD coupling constant at
finite temperature and the crossover between bulk and surface critical
behaviour in a semi-infinite geometry are considered.Comment: 17 pages LaTex; to be published in the Proceedings of RG '96, Dubn
An investigation of the relationship between rumination styles, hope, and suicide ideation through the lens of the integrated motivational-volitional model of suicidal behavior
To investigate the roles specific ruminative styles (brooding and reflection) and hope play in the Integrated Motivational-Volitional (IMV) model of suicidal behavior. Participants were students from a large U.S. state university who were selectively sampled for the experience of recent suicide ideation. Results of a bootstrapped moderated mediation model indicated that defeat had a direct effect on suicide ideation but not an indirect effect on suicide ideation through entrapment. Brooding, but not reflection, strengthened the relationship between defeat and entrapment. Hope weakened the relationship between entrapment and suicide ideation. Implications for the assessment and treatment of suicide risk and future research directions are discussed
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]
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
Gamble mode: Resonance contact mode in atomic force microscopy
Active noise reduction has been accomplished in atomic force microscopy by applying a high frequency, low amplitude vibration to the cantilever while it is in contact with a surface. The applied excitation (>~ 200 kHz; ~ 1 nm) is acoustically coupled to the tip and dampens the resonance Q factors of the system. The applied frequency is well above the bandwidth of the acquisition system (50 kHz). We call this mode "gamble mode" or "resonance contact.
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