41 research outputs found
Thin Fisher zeros
Various authors have suggested that the loci of partition function zeros can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeros for Ising and Potts models on non-planar ('thin') regular random graphs using this approach, and note that the locus of Fisher zeros on a Bethe lattice is identical to the corresponding random graph. Since the number of states q appears as a parameter in the Potts solution the limiting locus of chromatic zeros is also accessible
Kertesz on Fat Graphs?
The identification of phase transition points, beta_c, with the percolation
thresholds of suitably defined clusters of spins has proved immensely fruitful
in many areas of statistical mechanics. Some time ago Kertesz suggested that
such percolation thresholds for models defined in field might also have
measurable physical consequences for regions of the phase diagram below beta_c,
giving rise to a ``Kertesz line'' running between beta_c and the bond
percolation threshold, beta_p, in the M, beta plane.
Although no thermodynamic singularities were associated with this line it
could still be divined by looking for a change in the behaviour of high-field
series for quantities such as the free energy or magnetisation. Adler and
Stauffer did precisely this with some pre-existing series for the regular
square lattice and simple cubic lattice Ising models and did, indeed, find
evidence for such a change in high-field series around beta_p. Since there is a
general dearth of high-field series there has been no other work along these
lines.
In this paper we use the solution of the Ising model in field on planar
random graphs by Boulatov and Kazakov to carry out a similar exercise for the
Ising model on random graphs (i.e. coupled to 2D quantum gravity). We generate
a high-field series for the Ising model on random graphs and examine
its behaviour for evidence of a Kertesz line
Fat and Thin Fisher Zeroes
We show that it is possible to determine the locus of Fisher zeroes in the
thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs
and their dual quadrangulations by matching up the real part of the high- and
low-temperature branches of the expression for the free energy. Similar methods
work for the mean-field model on generic, ``thin'' graphs. Series expansions
are very easy to obtain for such random graph Ising models.Comment: 3 pages, LaTeX, Lattice2001(surfaces
Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations
A consistent theory of quantum gravity (QG) at Planck scale almost sure
contains manifestations of Lorentz local symmetry violations (LV) which may be
detected at observable scales. This can be effectively described and classified
by models with nonlinear dispersions and related Finsler metrics and
fundamental geometric objects (nonlinear and linear connections) depending on
velocity/ momentum variables. We prove that the trapping brane mechanism
provides an accurate description of gravitational and matter field phenomena
with LV over a wide range of distance scales and recovering in a systematic way
the general relativity (GR) and local Lorentz symmetries. In contrast to the
models with extra spacetime dimensions, the Einstein-Finsler type gravity
theories are positively with nontrivial nonlinear connection structure,
nonholonomic constraints and torsion induced by generic off-diagonal
coefficients of metrics, and determined by fundamental QG and/or LV effects.Comment: latex2e, 11pt, 34 pages, the version accepted to Class. Quant. Gra
The General Very Special Relativity in Finsler Cosmology
General Very Special Relativity (GVSR) is the curved space-time of Very
Special Relativity (VSR) proposed by Cohen and Glashow. The geometry of GVSR
possesses a line element of Finsler Geometry proposed by Bogoslovsky. We
calculate the Einstein field equations and derive a modified FRW cosmology, for
an osculating Riemannian space. The Friedman equation of motion leads to an
explanation of the cosmological acceleration in terms of an alternative
non-Lorentz invariant theory. A first order approach for a primordial spurionic
vector field introduced into the metric, gives back an estimation of the energy
evolution and inflationComment: 14 pages- accepted to Physical Review
Fat Fisher Zeroes
We show that it is possible to determine the locus of Fisher zeroes in the
thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs
and their dual quadrangulations by matching up the real part of the high and
low temperature branches of the expression for the free energy. The form of
this expression for the free energy also means that series expansion results
for the zeroes may be obtained with rather less effort than might appear
necessary at first sight by simply reverting the series expansion of a function
g(z) which appears in the solution and taking a logarithm.
Unlike regular 2D lattices where numerous unphysical critical points exist
with non-standard exponents, the Ising model on planar phi4 graphs displays
only the physical transition at c = exp (- 2 beta) = 1/4 and a mirror
transition at c=-1/4 both with KPZ/DDK exponents (alpha = -1, beta = 1/2, gamma
= 2). The relation between the phi4 locus and that of the dual quadrangulations
is akin to that between the (regular) triangular and honeycomb lattices since
there is no self-duality.Comment: 12 pages + 6 eps figure
Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
A generalized model of space-time is given, taking into consideration the
anisotropic structure of fields which are depended on the position and the
direction (velocity).In this framework a generalized FRW-metric the
Raychaudhouri and Friedmann equations are studied.A long range vector field of
cosmological origin is considered in relation to the physical geometry of
space-time in which Cartan connection has a fundamental role.The generalised
Friedmann equations are produced including anisotropic terms.The variation of
anisotropy is expressed in terms of the Cartan torsion tensor of the
Finslerian space-time.A possible estimation of the anisotropic parameter
can be achieved with the aid of the de-Sitter model of the empty flat universe
with weak anisotropy. Finally a physical generalisation for the model of
inflation is also studied.Comment: 21 pages- to appear in GR
(Re) defining salesperson motivation: current status, main challenges, and research directions
The construct of motivation is one of the central themes in selling and sales management research. Yet, to-date no review article exists that surveys the construct (both from an extrinsic and intrinsic motivation context), critically evaluates its current status, examines various key challenges apparent from the extant research, and suggests new research opportunities based on a thorough review of past work. The authors explore how motivation is defined, major theories underpinning motivation, how motivation has historically been measured, and key methodologies used over time. In addition, attention is given to principal drivers and outcomes of salesperson motivation. A summarizing appendix of key articles in salesperson motivation is provided
General very special relativity in Finsler cosmology
General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation. © 2009 The American Physical Society