41 research outputs found
A classification of four-state spin edge Potts models
We classify four-state spin models with interactions along the edges
according to their behavior under a specific group of symmetry transformations.
This analysis uses the measure of complexity of the action of the symmetries,
in the spirit of the study of discrete dynamical systems on the space of
parameters of the models, and aims at uncovering solvable ones. We find that
the action of these symmetries has low complexity (polynomial growth, zero
entropy). We obtain natural parametrizations of various models, among which an
unexpected elliptic parametrization of the four-state chiral Potts model, which
we use to localize possible integrability conditions associated with high genus
curves.Comment: 5 figure
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
Random Matrix Theory and higher genus integrability: the quantum chiral Potts model
We perform a Random Matrix Theory (RMT) analysis of the quantum four-state
chiral Potts chain for different sizes of the chain up to size L=8. Our
analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics,
suggesting the existence of a generalized time-reversal invariance.
Furthermore a change from the (generic) GOE distribution to a Poisson
distribution occurs when the integrability conditions are met. The chiral Potts
model is known to correspond to a (star-triangle) integrability associated with
curves of genus higher than zero or one. Therefore, the RMT analysis can also
be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure
First-order transition features of the 3D bimodal random-field Ising model
Two numerical strategies based on the Wang-Landau and Lee entropic sampling
schemes are implemented to investigate the first-order transition features of
the 3D bimodal () random-field Ising model at the strong disorder
regime. We consider simple cubic lattices with linear sizes in the range
and simulate the system for two values of the disorder strength:
and . The nature of the transition is elucidated by applying the
Lee-Kosterlitz free-energy barrier method. Our results indicate that, despite
the strong first-order-like characteristics, the transition remains continuous,
in disagreement with the early mean-field theory prediction of a tricritical
point at high values of the random-field.Comment: 19 pages, 6 figures, slightly extended version as accepted for
publicatio
Critical aspects of the random-field Ising model
We investigate the critical behavior of the three-dimensional random-field Ising model
(RFIM) with a Gaussian field distribution at zero temperature. By implementing a
computational approach that maps the ground-state of the RFIM to the maximum-flow
optimization problem of a network, we simulate large ensembles of disorder realizations of
the model for a broad range of values of the disorder strength h and
system sizes  = L3, with L â€Â 156. Our averaging procedure
outcomes previous studies of the model, increasing the sampling of ground states by a
factor of 103. Using well-established finite-size scaling schemes, the
fourth-orderâs Binder cumulant, and the sample-to-sample fluctuations of various
thermodynamic quantities, we provide high-accuracy estimates for the critical field
hc, as well as the critical exponents Μ,
ÎČ/Îœ, and ÎłÌ
/Μ of the correlation length, order parameter, and
disconnected susceptibility, respectively. Moreover, using properly defined noise to
signal ratios, we depict the variation of the self-averaging property of the model, by
crossing the phase boundary into the ordered phase. Finally, we discuss the controversial
issue of the specific heat based on a scaling analysis of the bond energy, providing
evidence that its critical exponent α â 0â
Exploring the ingredients required to successfully model the placement, generation, and evolution of ice streams in the British-Irish Ice Sheet
Ice stream evolution is a major uncertainty in projections of the future of the Greenland and Antarctic Ice sheets. Accurate simulation of ice stream evolution requires an understanding of a number of âingredientsâ that control the location and behaviour of ice stream flow. Here, we test the influence of geothermal heat flux, grid resolution, and bed hydrology on simulated ice streaming. The palaeo-record provides snapshots of ice stream evolution, with a particularly well constrained ice sheet being the British-Irish Ice Sheet (BIIS). We implement a new basal sliding scheme coupled with thermo-mechanics into the BISICLES ice sheet model, to simulate the evolution of the BIIS ice streams. We find that the simulated location and spacing of ice streams matches well with the empirical reconstructions of ice stream flow in terms of position and direction when simple bed hydrology is included. We show that the new basal sliding scheme allows the accurate simulation for the majority of BIIS ice streams. The extensive empirical record of the BIIS has allowed the testing of model inputs, and has helped demonstrate the skill of the ice sheet model in simulating the evolution of the location, spacing, and migration of ice streams through millennia. Simulated ice streams also prompt new empirical mapping of features indicative of streaming in the North Channel region. Ice sheet model development has allowed accurate simulation of the palaeo record, and allows for improved modelling of future ice stream behaviour
Global link between deformation and volcanic eruption quantified by satellite imagery
A key challenge for volcanological science and hazard management is that few of the worldâs volcanoes are effectively monitored. Satellite imagery covers volcanoes globally throughout their eruptive cycles, independent of ground-based monitoring, providing a multidecadal archive suitable for probabilistic analysis linking deformation with eruption. Here we show that, of the 198 volcanoes systematically observed for the past 18 years, 54 deformed, of which 25 also erupted. For assessing eruption potential, this high proportion of deforming volcanoes that also erupted (46%), together with the proportion of non-deforming volcanoes that did not erupt (94%), jointly represent indicators with âstrongâ evidential worth. Using a larger catalogue of 540 volcanoes observed for 3 years, we demonstrate how this eruptionâdeformation relationship is influenced by tectonic, petrological and volcanic factors. Satellite technology is rapidly evolving and routine monitoring of the deformation status of all volcanoes from space is anticipated, meaning probabilistic approaches will increasingly inform hazard decisions and strategic development