904 research outputs found
Energy Landscape Statistics of the Random Orthogonal Model
The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a
model of statistical mechanics where the couplings among the spins are defined
by a matrix chosen randomly within the orthogonal ensemble. It reproduces the
most relevant properties of the Parisi solution of the Sherrington-Kirckpatrick
model. Here we compute the energy distribution, and work out an extimate for
the two-point correlation function. Moreover, we show exponential increase of
the number of metastable states also for non zero magnetic field.Comment: 23 pages, 6 figures, submitted to J. Phys.
Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks
We review here some general properties of antiferromagnetic Heisenberg spin
chains, emphasizing and discussing the role of hidden symmetries in the
classification of the various phases of the models. We present also some recent
results that have been obtained with a combined use of Conformal Field Theory
and of numerical Density Matrix Renormalization Group techniques.Comment: To be published in the proceedings of the XIII Conference on
"Symmetries in Physics", held in Bregenz (Voralberg, Austria), 21-24/7/2003.
Plain LaTeX2e, 4 EPS figure
Thermodynamical Limit for Correlated Gaussian Random Energy Models
Let \{E_{\s}(N)\}_{\s\in\Sigma_N} be a family of centered
unit Gaussian random variables defined by the covariance matrix of
elements \displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}, and H_N(\s)
= - \sqrt{N} E_{\s}(N) the corresponding random Hamiltonian. Then the quenched
thermodynamical limit exists if, for every decomposition , and all
pairs (\s,\t)\in \Sigma_N\times \Sigma_N: c_N(\s,\tau)\leq \frac{N_1}{N}
c_{N_1}(\pi_1(\s),\pi_1(\tau))+ \frac{N_2}{N} c_{N_2}(\pi_2(\s),\pi_2(\tau))
where \pi_k(\s), k=1,2 are the projections of \s\in\Sigma_N into
. The condition is explicitly verified for the
Sherrington-Kirckpatrick, the even -spin, the Derrida REM and the
Derrida-Gardner GREM models.Comment: 15 pages, few remarks and two references added. To appear in Commun.
Math. Phy
Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour
We consider the zero-temperature dynamics for the infinite-range, non
translation invariant one-dimensional spin model introduced by Marinari, Parisi
and Ritort to generate glassy behaviour out of a deterministic interaction. It
is shown that there can be a large number of metatastable (i.e., one-flip
stable) states with very small overlap with the ground state but very close in
energy to it, and that their total number increases exponentially with the size
of the system.Comment: 25 pages, 8 figure
On critical phases in anisotropic spin-1 chains
Quantum spin-1 chains may develop massless phases in presence of Ising-like
and single-ion anisotropies. We have studied c=1 critical phases by means of
both analytical techniques, including a mapping of the lattice Hamiltonian onto
an O(2) nonlinear sigma model, and a multi-target DMRG algorithm which allows
for accurate calculation of excited states. We find excellent quantitative
agreement with the theoretical predictions and conclude that a pure Gaussian
model, without any orbifold construction, describes correctly the low-energy
physics of these critical phases. This combined analysis indicates that the
multicritical point at large single-ion anisotropy does not belong to the same
universality class as the Takhtajan-Babujian Hamiltonian as claimed in the
past. A link between string-order correlation functions and twisting vertex
operators, along the c=1 line that ends at this point, is also suggested.Comment: 9 pages, 3 figures, svjour format, submitted to Eur. Phys. J.
Effective mapping of spin-1 chains onto integrable fermionic models. A study of string and Neel correlation functions
We derive the dominant contribution to the large-distance decay of
correlation functions for a spin chain model that exhibits both Haldane and
Neel phases in its ground state phase diagram. The analytic results are
obtained by means of an approximate mapping between a spin-1 anisotropic
Hamiltonian onto a fermionic model of noninteracting Bogolioubov quasiparticles
related in turn to the XY spin-1/2 chain in a transverse field. This approach
allows us to express the spin-1 string operators in terms of fermionic
operators so that the dominant contribution to the string correlators at large
distances can be computed using the technique of Toeplitz determinants. As
expected, we find long-range string order both in the longitudinal and in the
transverse channel in the Haldane phase, while in the Neel phase only the
longitudinal order survives. In this way, the long-range string order can be
explicitly related to the components of the magnetization of the XY model.
Moreover, apart from the critical line, where the decay is algebraic, we find
that in the gapped phases the decay is governed by an exponential tail
multiplied by algebraic factors. As regards the usual two points correlation
functions, we show that the longitudinal one behaves in a 'dual' fashion with
respect to the transverse string correlator, namely both the asymptotic values
and the decay laws exchange when the transition line is crossed. For the
transverse spin-spin correlator, we find a finite characteristic length which
is an unexpected feature at the critical point. We also comment briefly the
entanglement features of the original system versus those of the effective
model. The goodness of the approximation and the analytical predictions are
checked versus density-matrix renormalization group calculations.Comment: 28 pages, plain LaTeX, 2 EPS figure
Deterministic spin models with a glassy phase transition
We consider the infinite-range deterministic spin models with Hamiltonian
, where is the quantization of a
chaotic map of the torus. The mean field (TAP) equations are derived by summing
the high temperature expansion. They predict a glassy phase transition at the
critical temperature .Comment: 8 pages, no figures, RevTex forma
PCV83 ADHERENCE WITH ANTIHYPERTENSIVE DRUG TREATMENT: EVIDENCE FROM PRIMARY CARE PRACTICE IN ITALY
Folds and Buckles at the Nanoscale: Experimental and Theoretical Investigation of the Bending Properties of Graphene Membranes
The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations
Phase separation and pairing regimes in the one-dimensional asymmetric Hubbard model
We address some open questions regarding the phase diagram of the
one-dimensional Hubbard model with asymmetric hopping coefficients and balanced
species. In the attractive regime we present a numerical study of the passage
from on-site pairing dominant correlations at small asymmetries to
charge-density waves in the region with markedly different hopping
coefficients. In the repulsive regime we exploit two analytical treatments in
the strong- and weak-coupling regimes in order to locate the onset of phase
separation at small and large asymmetries respectively.Comment: 13 pages, RevTeX 4, 12 eps figures, some additional refs. with
respect to v1 and citation errors fixe
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