36 research outputs found
The 3-d Random Field Ising Model at zero temperature
We study numerically the zero temperature Random Field Ising Model on cubic
lattices of various linear sizes in three dimensions. For each random field
configuration we vary the ferromagnetic coupling strength . We find that in
the infinite volume limit the magnetization is discontinuous in . The energy
and its first derivative are continuous. The approch to the thermodynamic
limit is slow, behaving like with for the gaussian
distribution of the random field. We also study the bimodal distribution , and we find similar results for the magnetization but with a
different value of the exponent . This raises the question of the
validity of universality for the random field problem.Comment: 8 pages, 3 PostScript Figure
Critical and tricritical singularities of the three-dimensional random-bond Potts model for large
We study the effect of varying strength, , of bond randomness on the
phase transition of the three-dimensional Potts model for large . The
cooperative behavior of the system is determined by large correlated domains in
which the spins points into the same direction. These domains have a finite
extent in the disordered phase. In the ordered phase there is a percolating
cluster of correlated spins. For a sufficiently large disorder
this percolating cluster coexists with a percolating cluster
of non-correlated spins. Such a co-existence is only possible in more than two
dimensions. We argue and check numerically that is the tricritical
disorder, which separates the first- and second-order transition regimes. The
tricritical exponents are estimated as and
. We claim these exponents are independent, for sufficiently
large . In the second-order transition regime the critical exponents
and are independent of the strength of
disorder.Comment: 12 pages, 11 figure
Complexity spectrum of some discrete dynamical systems
We first study birational mappings generated by the composition of the matrix
inversion and of a permutation of the entries of matrices. We
introduce a semi-numerical analysis which enables to compute the Arnold
complexities for all the possible birational transformations. These
complexities correspond to a spectrum of eighteen algebraic values. We then
drastically generalize these results, replacing permutations of the entries by
homogeneous polynomial transformations of the entries possibly depending on
many parameters. Again it is shown that the associated birational, or even
rational, transformations yield algebraic values for their complexities.Comment: 1 LaTex fil
Disorder driven phase transitions of the large q-state Potts model in 3d
Phase transitions induced by varying the strength of disorder in the large-q
state Potts model in 3d are studied by analytical and numerical methods. By
switching on the disorder the transition stays of first order, but different
thermodynamical quantities display essential singularities. Only for strong
enough disorder the transition will be soften into a second-order one, in which
case the ordered phase becomes non-homogeneous at large scales, while the
non-correlated sites percolate the sample. In the critical regime the critical
exponents are found universal: \beta/\nu=0.60(2) and \nu=0.73(1).Comment: 4 pages; 3 figure
The proposed dropping of the genus crassostrea for all Pacific cupped oysters and its replacement by a new genus magallana: a dissenting view
The World Register of Marine Species (WoRMS) currently
registers all Pacific cupped oysters that were formerly members
of the genus Crassostrea in a new genus, Magallana. Magallana
gigas is designated as an ââaccepted name,ââ whereas a search for
Crassostrea gigas results in the message ââno matching results
found.ââ This has caused dismay among many biologists,
aquaculturists, and other stakeholders with an interest in the
Pacific and other oysters. This note, which is authored by 27
interested scientists, presents a dissenting view and a rebuttal of
the proposed change of genus
On the complexity of some birational transformations
Using three different approaches, we analyze the complexity of various
birational maps constructed from simple operations (inversions) on square
matrices of arbitrary size. The first approach consists in the study of the
images of lines, and relies mainly on univariate polynomial algebra, the second
approach is a singularity analysis, and the third method is more numerical,
using integer arithmetics. Each method has its own domain of application, but
they give corroborating results, and lead us to a conjecture on the complexity
of a class of maps constructed from matrix inversions
Integrability of the critical point of the Kagom\'e three-state Potts mode
The vicinity of the critical point of the three-state Potts model on a
Kagom\'e lattice is studied by mean of Random Matrix Theory. Strong evidence
that the critical point is integrable is given.Comment: 1 LaTex file + 3 eps files 7 page
Spectral Properties of Statistical Mechanics Models
The full spectrum of transfer matrices of the general eight-vertex model on a
square lattice is obtained by numerical diagonalization. The eigenvalue spacing
distribution and the spectral rigidity are analyzed. In non-integrable regimes
we have found eigenvalue repulsion as for the Gaussian orthogonal ensemble in
random matrix theory. By contrast, in integrable regimes we have found
eigenvalue independence leading to a Poissonian behavior, and, for some points,
level clustering. These first examples from classical statistical mechanics
suggest that the conjecture of integrability successfully applied to quantum
spin systems also holds for classical systems.Comment: 4 pages, 1 Revtex file and 4 postscript figures tarred, gzipped and
uuencode
Symmetry, complexity and multicritical point of the two-dimensional spin glass
We analyze models of spin glasses on the two-dimensional square lattice by
exploiting symmetry arguments. The replicated partition functions of the Ising
and related spin glasses are shown to have many remarkable symmetry properties
as functions of the edge Boltzmann factors. It is shown that the applications
of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate
reduced complexities when the elements of the matrix satisfy certain
conditions, suggesting that the system has special simplicities under such
conditions. Using these duality and symmetry arguments we present a conjecture
on the exact location of the multicritical point in the phase diagram.Comment: 32 pages, 6 figures; a few typos corrected. To be published in J.
Phys.