704 research outputs found
Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model
The scaling behaviour of the edge of the Lee--Yang zeroes in the four
dimensional Ising model is analyzed. This model is believed to belong to the
same universality class as the model which plays a central role in
relativistic quantum field theory. While in the thermodynamic limit the scaling
of the Yang--Lee edge is not modified by multiplicative logarithmic
corrections, such corrections are manifest in the corresponding finite--size
formulae. The asymptotic form for the density of zeroes which recovers the
scaling behaviour of the susceptibility and the specific heat in the
thermodynamic limit is found to exhibit logarithmic corrections too. The
density of zeroes for a finite--size system is examined both analytically and
numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP
20-11-9
The Weakly Coupled Gross-Neveu Model with Wilson Fermions
The nature of the phase transition in the lattice Gross-Neveu model with
Wilson fermions is investigated using a new analytical technique. This involves
a new type of weak coupling expansion which focuses on the partition function
zeroes of the model. Its application to the single flavour Gross-Neveu model
yields a phase diagram whose structure is consistent with that predicted from a
saddle point approach. The existence of an Aoki phase is confirmed and its
width in the weakly coupled region is determined. Parity, rather than chiral
symmetry breaking naturally emerges as the driving mechanism for the phase
transition.Comment: 15 pages including 1 figur
Fermion loop simulation of the lattice Gross-Neveu model
We present a numerical simulation of the Gross-Neveu model on the lattice
using a new representation in terms of fermion loops. In the loop
representation all signs due to Pauli statistics are eliminated completely and
the partition function is a sum over closed loops with only positive weights.
We demonstrate that the new formulation allows to simulate volumes which are
two orders of magnitude larger than those accessible with standard methods
The Fate of Ernst Ising and the Fate of his Model
On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv
(Ukraine), we give some personal reflections about the famous model that was
suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one
dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising
marked the start of a scientific direction that, over nearly 100 years,
delivered extraordinary successes in explaining collective behaviour in a vast
variety of systems, both within and beyond the natural sciences. The broadness
of the appeal of the Ising model is reflected in the variety of talks presented
at the Ising lectures ( http://www.icmp.lviv.ua/ising/ ) over the past two
decades but requires that we restrict this report to a small selection of
topics. The paper starts with some personal memoirs of Thomas Ising (Ernst's
son). We then discuss the history of the model, exact solutions, experimental
realisations, and its extension to other fields.Comment: 46 pages, 9 figure
Recommended from our members
Soil Characterization at the Linde FUSRAP Site and the Impact on Soil Volume Estimates
The former Linde site in Tonawanda, New York is currently undergoing active remediation of Manhattan Engineering District's radiological contamination. This remediation is authorized under the Formerly Utilized Sites Remedial Action Program (FUSRAP). The focus of this paper will be to describe the impact of soil characterization efforts as they relate to soil volume estimates and project cost estimates. An additional objective is to stimulate discussion about other characterization and modeling technologies, and to provide a ''Lessons Learned'' scenario to assist in future volume estimating at other FUSRAP sites. Initial soil characterization efforts at the Linde FUSRAP site in areas known to be contaminated or suspected to be contaminated were presented in the Remedial Investigation Report for the Tonawanda Site, dated February 1993. Results of those initial characterization efforts were the basis for soil volume estimates that were used to estimate and negotiate the current remediation contract. During the course of remediation, previously unidentified areas of contamination were discovered, and additional characterization was initiated. Additional test pit and geoprobe samples were obtained at over 500 locations, bringing the total to over 800 sample locations at the 135-acre site. New data continues to be collected on a routine basis during ongoing remedial actions
Ising spins coupled to a four-dimensional discrete Regge skeleton
Regge calculus is a powerful method to approximate a continuous manifold by a
simplicial lattice, keeping the connectivities of the underlying lattice fixed
and taking the edge lengths as degrees of freedom. The discrete Regge model
employed in this work limits the choice of the link lengths to a finite number.
To get more precise insight into the behavior of the four-dimensional discrete
Regge model, we coupled spins to the fluctuating manifolds. We examined the
phase transition of the spin system and the associated critical exponents. The
results are obtained from finite-size scaling analyses of Monte Carlo
simulations. We find consistency with the mean-field theory of the Ising model
on a static four-dimensional lattice.Comment: 19 pages, 7 figure
Griffiths singularities in the two dimensional diluted Ising model
We study numerically the probability distribution of the Yang-Lee zeroes
inside the Griffiths phase for the two dimensional site diluted Ising model and
we check that the shape of this distribution is that predicted in previous
analytical works. By studying the finite size scaling of the averaged smallest
zero at the phase transition we extract, for two values of the dilution, the
anomalous dimension, , which agrees very well with the previous estimated
values.Comment: 11 pages and 4 figures, some minor changes in Fig. 4, available at
http://chimera.roma1.infn.it/index_papers_complex.htm
The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for
nonequilibrium dynamics, in particular driven diffusive processes. It is
usually considered in a canonical ensemble in which the number of sites is
fixed. We observe that the grand-canonical partition function for the ASEP is
remarkably simple. It allows a simple direct derivation of the asymptotics of
the canonical normalization in various phases and of the correspondence with
One-Transit Walks recently observed by Brak et.al.Comment: Published versio
Quasi-long-range ordering in a finite-size 2D Heisenberg model
We analyse the low-temperature behaviour of the Heisenberg model on a
two-dimensional lattice of finite size. Presence of a residual magnetisation in
a finite-size system enables us to use the spin wave approximation, which is
known to give reliable results for the XY model at low temperatures T. For the
system considered, we find that the spin-spin correlation function decays as
1/r^eta(T) for large separations r bringing about presence of a
quasi-long-range ordering. We give analytic estimates for the exponent eta(T)
in different regimes and support our findings by Monte Carlo simulations of the
model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include
The Phases and Triviality of Scalar Quantum Electrodynamics
The phase diagram and critical behavior of scalar quantum electrodynamics are
investigated using lattice gauge theory techniques. The lattice action fixes
the length of the scalar (``Higgs'') field and treats the gauge field as
non-compact. The phase diagram is two dimensional. No fine tuning or
extrapolations are needed to study the theory's critical behovior. Two lines of
second order phase transitions are discovered and the scaling laws for each are
studied by finite size scaling methods on lattices ranging from through
. One line corresponds to monopole percolation and the other to a
transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent
specific heats. The lines of transitions cross in the interior of the phase
diagram and appear to be unrelated. The monopole percolation transition has
critical indices which are compatible with ordinary four dimensional
percolation uneffected by interactions. Finite size scaling and histogram
methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line
are well-fit by the hypothesis that scalar quantum electrodynamics is
logarithmically trivial. The logarithms are measured in both finite size
scaling of the specific heat peaks as a function of volume as well as in the
coupling constant dependence of the specific heats measured on fixed but large
lattices. The theory is seen to be qualitatively similar to .
The standard CRAY random number generator RANF proved to be inadequateComment: 25pages,26figures;revtex;ILL-(TH)-94-#12; only hardcopy of figures
availabl
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