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1.
We consider a system of multicolor disordered lattice gas in a hypercube of ℤ
d
. Using a recent result of Caputo (article in preparation), we give an estimate of the spectral gap for the nearest-neighbor
dynamics which plays an important role in the study of hydrodynamic limit. 相似文献
2.
S. Suwanna 《Journal of statistical physics》2009,136(6):1131-1175
We prove that a finite Trotter approximation to the averaged mean square distance traveled by a particle in a disordered system
on a lattice ℤ
d
exhibits at most a diffusive behavior in dimensions d≥3 as long as the Fourier transform of the single-site probability, [^(m)]\hat{\mu }, is in L
2(ℝ). 相似文献
3.
Let ℤ+
d
+1= ℤ+×ℤ+, let H
0 be the discrete Laplacian on the Hilbert space l
2(ℤ+
d
+1) with a Dirichlet boundary condition, and let V be a potential supported on the boundary ∂ℤ+
d
+1. We introduce the notions of surface states and surface spectrum of the operator H=H
0+V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on σ(H
0) with probability one. To prove this result we combine Aizenman–Molchanov theory with techniques of scattering theory.
Received: 18 September 2000 / Accepted: 21 November 2000 相似文献
4.
We study the stationary distribution of the standard Abelian sandpile model in the box Λn = [-n, n]
d
∩ ℤ
d
for d≥ 2. We show that as n→ ∞, the finite volume stationary distributions weakly converge to a translation invariant measure on allowed sandpile configurations
in ℤ
d
. This allows us to define infinite volume versions of the avalanche-size distribution and related quantities. The proof is
based on a mapping of the sandpile model to the uniform spanning tree due to Majumdar and Dhar, and the existence of the wired
uniform spanning forest measure on ℤ
d
. In the case d > 4, we also make use of Wilson’s method.
An erratum to this article is available at . 相似文献
5.
Vladislav Kargin 《Journal of statistical physics》2010,140(2):393-408
This paper is concerned with the continuous-time quantum walk on ℤ, ℤ
d
, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability
distribution for the general isotropic walk on ℤ, and for nearest-neighbor walks on ℤ
d
and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to
zero at time t in all these cases. 相似文献
6.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Communications in Mathematical Physics》2002,231(3):435-461
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ
d
× ℤ+, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ
n
(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n) ℤ
d
× ℤ+, summing this probability over x ℤ
d
, and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation
to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n
−1, we prove existence of a limiting measure ℚ∞, with ℚ∞ = ℙ∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension
of the cluster of the origin, under ℙ∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented
percolation to super-Brownian motion, for d+1 > 4+1.
Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl 相似文献
7.
A Fredholm Determinant Representation in ASEP 总被引:3,自引:2,他引:1
In previous work (Tracy and Widom in Commun. Math. Phys. 279:815–844, 2008) the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice
ℤ. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the
case of step initial condition with particles at the positive integers ℤ+ and consider the distribution function for the mth particle from the left. In Tracy and Widom (Commun. Math. Phys. 279:815–844, 2008) an infinite series of multiple integrals was derived for the distribution. In this note we show that the series can be summed
to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive
(non-rigorously, at this writing) a scaling limit. 相似文献
8.
I. Schmelzer 《Foundations of Physics》2009,39(1):73-107
We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice
space (Aff(3)⊗ℂ)(ℤ3). This space allows a simple physical interpretation as a phase space of a lattice of cells.
We find the SM SU(3)
c
×SU(2)
L
×U(1)
Y
action on (Aff(3)⊗ℂ⊗Λ)(ℝ3) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson
gauge fields and correction terms for lattice deformations.
The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ2-valued (spin) field theory.
A metric theory of gravity compatible with this model is presented too. 相似文献
9.
We consider an Euclidean supersymmetric field theory in ℤ3 given by a supersymmetric Φ4 perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green’s
function of a (stable) Lévy random walk in ℤ3. The Green’s function depends on the Lévy-Khintchine parameter
with 0<α<2. For
the Φ4 interaction is marginal. We prove for
sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory
uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on
all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this
theory comes from the easily established fact that the Green’s function of a (weakly) self-avoiding Lévy walk in ℤ3 is a second moment (two point correlation function) of the supersymmetric measure governing this model. The rigorous control
of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly)
self-avoiding Lévy walk in ℤ3. 相似文献
10.
We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models
on a lattice ℤ
d
. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a
suitably modified sublattice of ℤ
d
. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the
quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation
decay.
We illustrate our method on the hard-core and monomer-dimer models, on which we improve several earlier estimates. For example
we show that the exponential of the monomer-dimer coverings of ℤ3 belongs to the interval [0.78595,0.78599], improving best previously known estimate of [0.7850,0.7862] obtained in (Friedland
and Peled in Adv. Appl. Math. 34:486–522, 2005; Friedland et al. in J. Stat. Phys., 2009). Moreover, we show that given a target additive error ε>0, the computational effort of our method for these two models is (1/ε)
O(1)
both for the free energy and surface pressure values. In contrast, prior methods, such as the transfer matrix method, require
exp ((1/ε)
O(1)) computation effort. 相似文献
11.
12.
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras.
An example is the factorisation of matrices M
2(ℂ)=ℂℤ2·ℂℤ2. We also further extend the coalgebra version of theory introduced previously, to include frame resolutions and corresponding
covariant derivatives and torsions. As an example, we construct q-monopoles on all the Podleś quantum spheres S
2
q,s
.
Received: 25 September 1998 / Accepted: 23 February 2000 相似文献
13.
We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber
dynamics of the Ising model over ℤ
d
/nℤ
d
. The theorems derived in this paper describe a type of adiabatic dynamics for
l1(\mathbbRn+)\ell^{1}(\mathbb{R}^{n}_{+}) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with ℓ
2(ℂ
n
) norm preserving ones, i.e. gradually changing unitary dynamics in ℂ
n
. 相似文献
14.
We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on ℤ
d
for d≥3 when p, the probability of occupation of a bond, is sufficiently close to 1. Moreover, we prove that equi-decay surfaces are locally
analytic, strictly convex, with positive Gaussian curvature. 相似文献
15.
We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice ℤ
d
. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the
associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition
(which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order
transition in the mean- field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on ℤ
d
undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q≥3, the r-component cubic models with r≥4 and the O(N)-nematic liquid-crystal models with N≥3.
Received: 22 July 2002 / Accepted: 12 January 2003
Published online: 5 May 2003
RID="⋆"
ID="⋆" ? Copyright rests with the authors. Reproduction of the entire article for non-commercial purposes is permitted without
charge.
Communicated by J. Z.Imbrie 相似文献
16.
Mykhaylo Tyomkyn 《Journal of statistical physics》2012,148(6):1072-1075
We analyze the abelian sandpile model on ℤ d for the starting configuration of n particles in the origin and 2d−2 particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres (J. Stat. Phys. 198:143–159, 2010) that the radius of the toppled cluster of this configuration is O(n 1/d ). 相似文献
17.
P. Mathieu 《Journal of statistical physics》2008,130(5):1025-1046
We prove an almost sure invariance principle for a random walker among i.i.d. conductances in ℤ
d
, d≥2. We assume conductances are bounded from above but we do not require that they are bounded from below. 相似文献
18.
We study the rotor router model and two deterministic sandpile models. For the rotor router model in ℤ
d
, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds
in dimension 2 are known. A unified approach for these models with a new parameter h (the initial number of particles at each site), allows to prove a number of new limiting shape results in any dimension d≥1.
For the rotor router model, the limiting shape is a sphere for all values of h. For one of the sandpile models, and h=2d−2 (the maximal value), the limiting shape is a cube. For both sandpile models, the limiting shape is a sphere in the limit
h→−∞. Finally, we prove that the rotor router shape contains a diamond. 相似文献
19.
Martin Tautenhahn 《Journal of statistical physics》2011,144(1):60-75
We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method.
Our theorems extend earlier results on localization for the Anderson model on ℤ
d
. We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently
large disorder. 相似文献
20.
Stefan Grosskinsky Alexander A. Lovisolo Daniel Ueltschi 《Journal of statistical physics》2012,146(6):1105-1121
We study random spatial permutations on ℤ3 where each jump x↦π(x) is penalized by a factor e-T|| x-p(x)||2\mathrm{e}^{-T\| x-\pi (x)\|^{2}}. The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the lengths of such cycles are distributed according to Poisson-Dirichlet.
This can be explained heuristically using a stochastic coagulation-fragmentation process for long cycles, which is supported
by numerical data. 相似文献