1,235 research outputs found
Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
We examine the proposal made recently that the su(3) modular invariant
partition functions could be related to the geometry of the complex Fermat
curves. Although a number of coincidences and similarities emerge between them
and certain algebraic curves related to triangular billiards, their meaning
remains obscure. In an attempt to go beyond the su(3) case, we show that any
rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps
Modelling quasicrystals at positive temperature
We consider a two-dimensional lattice model of equilibrium statistical
mechanics, using nearest neighbor interactions based on the matching conditions
for an aperiodic set of 16 Wang tiles. This model has uncountably many ground
state configurations, all of which are nonperiodic. The question addressed in
this paper is whether nonperiodicity persists at low but positive temperature.
We present arguments, mostly numerical, that this is indeed the case. In
particular, we define an appropriate order parameter, prove that it is
identically zero at high temperatures, and show by Monte Carlo simulation that
it is nonzero at low temperatures
Generalized nonuniform dichotomies and local stable manifolds
We establish the existence of local stable manifolds for semiflows generated
by nonlinear perturbations of nonautonomous ordinary linear differential
equations in Banach spaces, assuming the existence of a general type of
nonuniform dichotomy for the evolution operator that contains the nonuniform
exponential and polynomial dichotomies as a very particular case. The family of
dichotomies considered allow situations for which the classical Lyapunov
exponents are zero. Additionally, we give new examples of application of our
stable manifold theorem and study the behavior of the dynamics under
perturbations.Comment: 18 pages. New version with minor corrections and an additional
theorem and an additional exampl
On the Thermodynamic Limit in Random Resistors Networks
We study a random resistors network model on a euclidean geometry \bt{Z}^d.
We formulate the model in terms of a variational principle and show that, under
appropriate boundary conditions, the thermodynamic limit of the dissipation per
unit volume is finite almost surely and in the mean. Moreover, we show that for
a particular thermodynamic limit the result is also independent of the boundary
conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty',
revised version to appear in Journal of Physics
Canonical solution of a system of long-range interacting rotators on a lattice
The canonical partition function of a system of rotators (classical X-Y
spins) on a lattice, coupled by terms decaying as the inverse of their distance
to the power alpha, is analytically computed. It is also shown how to compute a
rescaling function that allows to reduce the model, for any d-dimensional
lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees'
Comments it has been transferred to Phys. Rev. E, because of supposed no
general interest. Divided into sections, corrections in (5) and (20),
reference 5 updated. 8 pages 1 figur
Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom
For a simple model of chaotic dynamical systems with a large number of
degrees of freedom, we find that there is an ensemble of unstable periodic
orbits (UPOs) with the special property that the expectation values of
macroscopic quantities can be calculated using only one UPO sampled from the
ensemble. Evidence to support this conclusion is obtained by generating the
ensemble by Monte Carlo calculation for a statistical mechanical model
described by a space-time Hamiltonian that is expressed in terms of Floquet
exponents of UPOs. This result allows us to interpret the recent interesting
discovery that statistical properties of turbulence can be obtained from only
one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato
and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].Comment: 4 pages, 1 figure. In order to clarify generality of our result and
the role of a large number of degrees of freedom, a brief subsection was
adde
Interaction Flip Identities for non Centered Spin Glasses
We consider spin glass models with non-centered interactions and investigate
the effect, on the random free energies, of flipping the interaction in a
subregion of the entire volume. A fluctuation bound obtained by martingale
methods produces, with the help of integration by parts technique, a family of
polynomial identities involving overlaps and magnetizations
Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
We prove that for quantum lattice systems in d<=2 dimensions the addition of
quenched disorder rounds any first order phase transition in the corresponding
conjugate order parameter, both at positive temperatures and at T=0. For
systems with continuous symmetry the statement extends up to d<=4 dimensions.
This establishes for quantum systems the existence of the Imry-Ma phenomenon
which for classical systems was proven by Aizenman and Wehr. The extension of
the proof to quantum systems is achieved by carrying out the analysis at the
level of thermodynamic quantities rather than equilibrium states.Comment: This article presents the detailed derivation of results which were
announced in Phys. Rev. Lett. 103 (2009) 197201 (arXiv:0907.2419). v3
incorporates many corrections and improvements resulting from referee
comment
Crystalline ground states for classical particles
Pair interactions whose Fourier transform is nonnegative and vanishes above a
wave number K_0 are shown to give rise to periodic and aperiodic infinite
volume ground state configurations (GSCs) in any dimension d. A typical three
dimensional example is an interaction of asymptotic form cos(K_0 r)/r^4. The
result is obtained for densities rho >= rho_d where rho_1=K_0/2pi,
rho_2=(sqrt{3}/8)(K_0/pi)^2 and rho_3=(1/8sqrt{2})(K_0/pi)^3. At rho_d there is
a unique periodic GSC which is the uniform chain, the triangular lattice and
the bcc lattice for d=1,2,3, respectively. For rho>rho_d the GSC is nonunique
and the degeneracy is continuous: Any periodic configuration of density rho
with all reciprocal lattice vectors not smaller than K_0, and any union of such
configurations, is a GSC. The fcc lattice is a GSC only for rho>=(1/6
sqrt{3})(K_0/pi)^3.Comment: final versio
Some Applications of the Lee-Yang Theorem
For lattice systems of statistical mechanics satisfying a Lee-Yang property
(i.e., for which the Lee-Yang circle theorem holds), we present a simple proof
of analyticity of (connected) correlations as functions of an external magnetic
field h, for Re h > 0 or Re h < 0. A survey of models known to have the
Lee-Yang property is given. We conclude by describing various applications of
the aforementioned analyticity in h.Comment: 16 page
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