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1.
We consider a class of spin systems on ℤ
d
with vector valued spins (S
x
) that interact via the pair-potentials J
x,y
S
x
⋅S
y
. The interactions are generally spread-out in the sense that the J
x,y
's exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently
spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field
theory signals such a transition. As a consequence, e.g., in dimensions d≥3, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which
undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions d = 1,2 for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also
investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a
unique “state,” then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field
values and the states themselves converge to a product measure. 相似文献
2.
We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one-and two-dimensional substrates focusing
our analysis on the probability distribution function P(M,L) of the number M of maximal points (i.e., local “peaks”) of growing surfaces. Our analysis is based on two central results: (i) the proof
(presented here) of the fact that uniform one-dimensional ballistic growth process in the steady state can be mapped onto
“rise-and-descent” sequences in the ensemble of random permutation matrices; and (ii) the fact, established in Ref. [G. Oshanin
and R. Voituriez, J. Phys. A: Math. Gen. 37:6221 (2004)], that different characteristics of “rise-and-descent” patterns in random permutations can be interpreted in
terms of a certain continuous-space Hammersley-type process. For one-dimensional system we compute P(M,L) exactly and also present explicit results for the correlation function characterizing the enveloping surface. For surfaces
grown on 2d substrates, we pursue similar approach considering the ensemble of permutation matrices with long-ranged correlations.
Determining exactly the first three cumulants of the corresponding distribution function, we define it in the scaling limit
using an expansion in the Edgeworth series, and show that it converges to a Gaussian function as L → ∞. 相似文献
3.
The general expression for the static permittivity ε(q, 0) of the Coulomb system in the region of small wave vectors was derived based on exact limit relations. The relation obtained
describes the function ε(q, 0) in both “metal” and “dielectric” states of the Coulomb system. On this basis, the concept of the “true” dielectric is
introduced and the definition of the “true” screening length was discussed. Exact relations were derived for the function
ε(q, 0) in the region of small wave vectors q within the random phase approximation at an arbitrary degeneracy. 相似文献
4.
A. Gadomski 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,9(4):569-571
In this Rapid Note, we show that the problem of growth of molecular superlattice in a fully hydrated dipalmitoylphosphatidylcholine (DPPC) membrane
during the gel-to-subgel phase transformation process is a problem of time scale. There are, in fact, two time scales. The
first is an “integrated” or, in some sense, stagnant time scale, that reflects the well-known isotropic growth effect in the
d-dimensional space, but assigns the problem to be still in a category of Debye relaxation kinetics. The fraction of old (parent)
phase does not suit the Paley-Wiener criterion for relaxation functions, and the time behavior is exclusively due to the geometrical
characteristics of the kinetic process. The second (multi-instantaneous) time scale, in turn, is recognised to be a “broken”
(fractional time derivative) or memory-feeling (dynamic) scale, which carries some very essential physics of the phenomenon
under study, and classifies the problem to be of non-Debye (viz., stretched exponential) nature. It may, in principle, contain all the important effects, like small scale coexistence, presence
of collisions between domains, with possible annihilation and creation of domain boundaries, and/or a headgroup packing, hydration
against lipid mobility behavior, and finally, a multitude of quasi-crystalline states. It turns out, that within the range
of validity of the dynamic scale approximation proposed, the criterion for relaxation functions is very well fulfilled.
Received 30 November 1998 相似文献
5.
We consider the flat Robertson–Walker model in scalar-tensor theory proposed by Lau and Prokhovnik. In this model, the field
equations are solved by using “gamma-law” form of equation of state p=(γ−1)ρ, where the adiabatic parameter ‘gamma’ (γ) varies continuously as the universe expands. Our aim is to study how the adiabatic parameter γ should vary so that in the course of its evolution the universe goes through a transition from an inflationary to a radiation-dominated
phase. A unified one parameter function of γ has been considered to describe the two early phases of evolution of universe. The solutions show the power-law expansion
and cosmological constant is found to be positive and decreasing function of cosmic time. The solutions are compatible with
the Dirac’s large number hypothesis. The deceleration parameter has been presented in a unified manner in terms of scale factor,
which describes the inflation of the model. The nature of singularity and the physical properties have been discussed in details. 相似文献
6.
M. Loulidi 《Journal of statistical physics》2008,132(1):109-127
A one-dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential
dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a perturbative mean
field-like approach the broken particle-hole symmetry is highlighted and the phase diagram is studied in the parameter space
(α,β), where α and β represent respectively the injection rate and the extraction rate of particles. The model displays, as in the pure case,
high-density, low-density and maximum-current phases. All critical lines are determined analytically showing that the high-density
low-density first order phase transition occurs at α≠β. We show that the maximum-current phase extends its stability region as the disorder is increased and the usual
-decay of the density profile in this phase is universal. Assuming that some exact results for the disordered model on a ring
hold for a system with open boundaries, we derive some analytical results for platoon phase transition within the low-density
phase and we give an analytical expression of its corresponding critical injection rate α
*. As it was observed numerically (Bengrine et al. J. Phys. A: Math. Gen. 32:2527, [1999]), we show that the quenched disorder induces a cusp in the current-density relation at maximum flow in a certain region
of parameter space and determine the analytical expression of its slope. The results of numerical simulations we develop agree
with the analytical ones.
Regular associate of ICTP. 相似文献
7.
We report the first observation of “quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen in the
dissipation domain. Capillary waves have been driven by low-frequency random force. We have observed that the frequency spectrum
of surface elevation changes its dependence from power-like 〈|ηω2|〉 ∼ ω−2,8 at middle-frequency domain to “quasi-Planck” distribution ∼e
ω/ω
d
at higher frequencies. The frequency ω
d
is proportional to the boundary frequency between inertial interval and dissipation domain and it is scaled up with the increase
of driving force. 相似文献
8.
We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two “bond ordered phases”, one with local ferromagnetic order and another with local anti-ferromagnetic
order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted
by Domany, Schick and Swendsen [1]. This last result generalizes the result of van Enter and Shlosman [2] We argue that these
phenomena are quite general and should occur for a large class of potentials.
PACS number: 64.60.Cn, 75.10.Hk 相似文献
9.
We study the pinning-depinning phenomenon of a contact line on a solid surface decorated by a random array of nanometric structures.
For this purpose, we have investigated the contact angle hysteresis behaviour of six different wetting and non-wetting fluids
with surface tensions varying from 25 to 72mN m^-1. For low values of the areal density of defects φd, the hysteresis H increases linearly with φd indicating that “individual” defects pin the contact line. Then, from a given value of φd, the hysteresis H becomes to decrease with increasing φd, indicating a new kind of collective depinning. These two regimes were observed for all fluids used. In both cases, our experimental
results are compared with the theoretical predictions for contact angle hysteresis induced by single or multiple topographical
defects. We ascribe the decrease of H to the formation of cavities along the wetting front. 相似文献
10.
A “finite thickness lens” model for self-focusing (defocusing) in Kerr medium is presented. An on-axis normalization transmittance
formula is presented for arbitrary nonlinear phase shift for the finite thickness Kerr medium by introducing a nonlinear ABCD-matrix for the transition of a Gaussian beam from linear to non-linear medium, without complex calculation for the beam radius
at the far field aperture. The variation of the peak and valley transmittance difference is found to enhance linearly as the
phase shift at the focus increases by increasing the thickness of the medium. If the ratio of the Rayleigh istance divided
by the thickness of the medium (d/z0) is constant and small enough, the peak and valley transmittance difference stays constant. Finally, a qualitative formula
is presented to express the relationship between the system parameters and the on-axis phase shift at the focus.
相似文献
11.
E. J. Janse van Rensburg 《Journal of statistical physics》1997,88(1-2):177-200
Self-avoiding plaquette surfaces with a folding or bending fugacity are believed to undergo a “crumpling” transition from
a flaccid phase with branched polymer characteristics (corresponding to surfaces with a high degree of folding), to a “smooth”
phase (corresponding to surfaces faith a low degree of folding). I develop rigorous techniques in order to bound the free
energy of this model. In particular, the limiting free energy is proven to be positive for all positive values of the folding
fugacity. In addition, the existence of a nonanalyticity in the limiting free energy of a (nontrivial) subclass of surfaces
is proven. This implies the existence of a phase transition in this model, which I conjecture to be from a “flaccid” to a
“smooth” phase. 相似文献
12.
Hironobu Sakagawa 《Journal of statistical physics》2009,135(3):467-481
We consider the d+1-dimensional effective interface model of gradient type with a quadratic interaction potential and a self-potential. Without
the self-potential, the model coincides with the d-dimensional massless Gaussian field. We show that for an arbitrary repulsive self-potential which can be thought as interaction
of the interface with a “soft wall”, the field is pushed up at least to the same level when the original Gaussian field is
conditioned to be positive everywhere, namely the “hard wall” condition is imposed. 相似文献
13.
A. A. Ovchinnikov M. Ya. Ovchinnikova E. A. Plekhanov 《Journal of Experimental and Theoretical Physics》1999,88(2):356-369
The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap
in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which
is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence
bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that
there is a fairly wide range of doping with antiferromagnetic order in isolated CuO2 planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction
t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary,
depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and
yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to
the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points
of the phase space owing to the dielectrization of the Fermi boundary at k
x=±
k
y. The model with orthorhombic distortions and two peaks on the curve of T
c versus doping is discussed in connection with experimental data for the yttrium-based ceramic.
Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999) 相似文献
14.
Finite-size rounding of a first-order phase transition is studied in “block”- and “cylinder”-shaped ferromagnetic scalar spin
systems. Crossover in shape is investigated and the universal form of the rounded susceptibility peak is obtained. Scaling
forms on the low-temperature side of the critical point are considered both above and below the borderline dimensionality,d
>=4. A method of phenomenological renormalization, applicable to both odd and even field derivatives, is suggested and used
to estimate universal amplitudes for two-dimensional Ising models atT=Tc. 相似文献
15.
The phase transition “triangular lattice-vortex liquid” in layered high-T
c
superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting
layers in a high-T
c
Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the
vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands
which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T
c
584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force
increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice”
decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially
(≃70 K).
Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997) 相似文献
16.
We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation
of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase.
The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays
the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦.
Received 14 October 2002 Published online 14 February 2003
RID="a"
ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de 相似文献
17.
We consider a D-dimensional model of gravity with non-linear “scalar fields” as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n − 1 factor spaces are Ricci-flat, e.g. when one space M 1 of dimension d 1 > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically symmetric solutions is studied and a restricted version of “no-hair theorem” for black holes is proved. For the case d 1 = 2 a subclass of latent soliton solutions is singled out. 相似文献
18.
M. V. Tokarev I. Zborovský A. Kechechyan A. Alakhverdyants 《Physics of Particles and Nuclei Letters》2011,8(6):533-541
The general concepts in the critical phenomena related with the notions of “scaling” and “universality” are considered. Behavior
of various systems near a phase transition is displayed. Search for clear signatures of the phase transition of the nuclear
matter and location of the critical point in heavy-ion collisions (HIC) is discussed. The experimental data on inclusive spectra measured in HIC at RHIC and SPS over a wide range of energies s
N N
1/2 = 9–200 GeV are analyzed in the framework of z-scaling. A microscopic scenario of the constituent interactions is presented. Dependence of the energy loss on the momentum
of the produced hadron, energy and centrality of the collision is studied. Self-similarity of the constituent interactions
described in terms of momentum fractions is used to characterize the nuclear medium by “specific heat” and colliding nuclei
by fractal dimensions. Preferable kinematical regions to search for signatures of the phase transition of the nuclear matter
produced in HIC are discussed. Discontinuity of the “specific heat” is assumed to be a signature of the phase transition and the critical
point. 相似文献
19.
We consider the branching and annihilating random walk and with reaction rates σ and λ, respectively, and hopping rate D, and study the phase diagram in the λ/D,σ/D) plane. According to standard mean-field theory, this system is in an active state for all σ/D≥0, and perturbative renormalization suggests that this mean-field result is valid for d>2; however, nonperturbative renormalization predicts that for all d there is a phase transition line to an absorbing state in the λ/D,σ/D) plane. We show here that a simple single-site approximationreproduces with minimal effort the nonperturbative phase diagram both qualitatively and quantitatively for all dimensions d>2. We expect the approach to be useful for other reaction-diffusion processes involving absorbing state transitions. 相似文献
20.
Cécile Monthus 《Letters in Mathematical Physics》2006,78(3):207-233
After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local transition rules, and on ‘polymer models’, where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points: thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures T
c(i,L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland–Scheraga model of DNA denaturation.Conference Proceedings “Mathematics and Physics”, I.H.E.S., France, November 2005 相似文献