共查询到20条相似文献,搜索用时 31 毫秒
1.
We study the finite size effects on Bose–Einstein condensation (BEC) of an ideal non-relativistic Bose gas in the three-sphere (spatial section of the Einstein universe) and in a partially finite box which is infinite in two of the spatial directions (infinite slab). Using the framework of grand-canonical statistics, we consider the number of particles, the condensate fraction and the specific heat. After obtaining asymptotic expansions for large system size, which are valid throughout the BEC regime, we describe analytically how the thermodynamic limit behaviour is approached. In particular, in the critical region of the BEC transition, we express the chemical potential and the specific heat as simple explicit functions of the temperature, highlighting the effects of finite size. These effects are seen to be different for the two different geometries. We also consider the Bose gas in a one-dimensional box, a system which does not possess BEC in the sense of a phase transition even in the infinite volume limit. 相似文献
2.
We investigated temperature dependent optical spectra of the one-dimensional chain compound Sr2CuO3. The charge transfer transition polarized along the chain direction shows a strongly asymmetric line shape as expected in one-dimensional extended Hubbard model. At low temperature, the charge transfer peak shows a large blueshift and reveals additional sharp peaks at the gap. Even though many spectroscopic studies suggest that this material cannot have a bound exciton based on the one-dimensional extended Hubbard model, we attribute the additional sharp peaks to excitons, which come to exist due to the long-range Coulomb interaction. 相似文献
3.
Michelle Przedborski 《Phase Transitions》2013,86(1):85-93
For the spin models with continuous symmetry on regular lattices and finite range of interactions, the lower critical dimension is d?=?2. In two dimensions the classical XY-model displays Berezinskii–Kosterlitz–Thouless (BKT) transition associated with unbinding of topological defects (vortices and antivortices). We perform a Monte Carlo study of the classical XY-model on Sierpiński pyramids (SPs) whose fractal dimension is D = log?4/log?2?=?2 and the average coordination number per site is ≈ 7. The specific heat does not depend on the system size which indicates the absence of a long-range order. From the dependence of the helicity modulus on the cluster size and on boundary conditions, we draw a conclusion that in the thermodynamic limit there is no BKT transition at any finite temperature. This conclusion is also supported by our results for linear magnetic susceptibility. The lack of finite temperature phase transition is presumably caused by the finite order of ramification of SP. 相似文献
4.
K. P. Schmidt A. Reischl G. S. Uhrig 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,38(2):343-352
In this work we give a consistent picture of the thermodynamic properties of
bosons in the Mott insulating phase when loaded adiabatically into
one-dimensional optical lattices. We find a crucial dependence of the
temperature in the optical lattice on the doping level of the Mott
insulator. In the undoped case, the temperature is of the order of the large
onsite
Hubbard interaction. In contrast, at a finite doping level the
temperature jumps almost immediately to the order of the small hopping
parameter. These two situations are investigated on the one hand by considering
limiting cases like the atomic limit and the case of free fermions. On the
other hand, they are examined using a quasi-particle conserving continuous
unitary transformation extended by an approximate thermodynamics for
hardcore particles. 相似文献
5.
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct dependence on the upper cutoff kc of the degree distribution. Since the infinite network limit can be obtained by allowing kc to diverge with the system size in an arbitrary way, this result implies that there are different routes to the thermodynamic limit in scale-free networks. The contact process (in its mean-field version) belongs to this second class and thus our results clarify the recent discrepancy between theory and simulations with different scaling of kc reported in the literature. 相似文献
6.
Using the various functional relations for correlation functions in planar Ising models, new results are obtained for the correlation functions and the q-dependent susceptibility for Ising models on a quadratic lattice with quasiperiodic coupling constants. The effects are clearest if the interactions are both attractive and repulsive according to a quasiperiodic pattern. In particular, an exact scaling limit result for the two-point correlation function of the Z-invariant inhomogeneous Ising model is presented and the q-dependent susceptibility is calculated for some cases where the coupling constants vary according to Fibonacci rules. It is found that the ferromagnetic case differs drastically from the case with both ferro- and antiferromagnetic bonds. In the mixed case, the peaks of the q-dependent susceptibility are everywhere dense for temperature T both above or below the critical temperature Tc, but due to overlap only a finite number of peaks is visible. This number of visible peaks decreases as T moves away from Tc. In the ferromagnetic case, there is typically only one single peak at q=0, in spite of the aperiodicity present in the lattice. These results provide evidence that in real systems, even if the atoms arrange themselves aperiodically, there will be no dramatic difference in the diffraction pattern, unless the pair correlation function has clear aperiodic oscillations. The number of oscillations per correlation length determines the number of visible peaks. 相似文献
7.
《Nuclear Physics B》1998,516(3):501-528
The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system, which we call the phase model, is the strong coupling limit of the integrable q-boson hopping model. The results are presented as determinants. 相似文献
8.
A chain of one-dimensional oscillators is considered. They are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors. The total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures. The stationary measures are obtained when the chain is finite; the thermodynamic limit is then considered, approach to the Gibbs distribution is proven, and a linear temperature profile is obtained. 相似文献
9.
10.
Basile AG Dumont RS 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(2):2015-2023
Using a numerical algorithm based on the time evolution of normal modes, we calculate the coefficient of restitution eta for various one-dimensional harmonic solids colliding with a hard wall. We find that, for a homogeneous chain, eta=1 in the thermodynamic limit. However, for a chain in which weaker springs are introduced in the colliding front half, eta remains significantly less than one even in the thermodynamic limit, and the "lost" energy goes mostly into low frequency normal modes. An understanding of these results is given in terms of how the energy is redistributed among the normal modes as the chain collides with the wall. We then contrast these results with those for collisions of one-dimensional harmonic solids with a soft wall. Using perturbation theory, we find that eta=1 for all harmonic chains in the extremely soft wall limit, but that inelasticity grows with increasing chain size in contrast to hard wall collisions. 相似文献
11.
We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data. 相似文献
12.
《Nuclear Physics B》1996,479(3):663-682
We obtain an effective potential of the O(N)-symmetric ø4 theory for large N starting with a finite lattice system and taking the thermodynamic limit with great care. In the thermodynamic limit, it is globally real-valued and convex in both the symmetric and the broken phases. In particular, it has a flat bottom in the broken phase. Taking the continuum limit, we discuss renormalization effects to the flat bottom and exhibit the effective potential of the continuum theory in three and four dimensions. On the other hand, the effective potential is nonconvex in a finite lattice system. Our numerical study shows that the barrier height of the effective potential flattens as a linear size of the system becomes large. It decreases obeying a power law and the exponent is about −2. The result is clearly understood from the dominance of configurations with a slowly-rotating field in one direction. 相似文献
13.
We use Gauss' principle of least constraint to impose different kinetic temperatures on the two halves of a periodic one-dimensional chain. The thermodynamic result is heat flow, as predicted by the Second Law of Thermodynamics. The statistical-mechanical result can be either a phase-space limit cycle or a strange attractor, depending on the chain length and the size of the temperature difference. We document the sensitivity of the Lyapunov spectrum and the underlying phase-space topology by varying the chain length and the size of the kinetic-temperature difference. 相似文献
14.
Eberth Correa Alvaro Ferraz 《The European Physical Journal B - Condensed Matter and Complex Systems》2014,87(3):1-9
In this paper we propose a Heisenberg variational approach to study pseudo-critical phenomena on ferromagnetic nanostructures. We combine a two-spin cluster 3-dimensional Heisenberg Hamiltonian with Orstein-Zernike correlations and consider several geometries and crystalline lattices to explore the relationship among these factors and the effective number of nearest neighbors defined in several kind of nanometric structures. With this method we examine the size at which the pseudo-critical temperature of a magnetic nanoparticle reaches its bulk value. Our results shed light on the nanoscopic-microscopic limit, evidencing in particular that when one dimension is very small, independently of how big the other dimensions become, it is not possible for the structure to reach the bulk-like behavior. The results of our model are in good agreement with experimental data and other available analytical models. 相似文献
15.
We propose two simplified models in order to discuss the origin of the Peierls transition in one-dimensional systems. For the finite-mode model we show that the thermodynamic properties are described correctly by the most general mean field approximation. But the discussion of the zero-bandwidth model suggests that this result is probably due to the fact of taking into account only a finite number of phonon modes even in the thermodynamic limit. 相似文献
16.
Thermodynamic properties of the spin-1/2 ferromagnetic Heisenberg chain with long-range interactions
The one-dimensional spin-1/2 XYZ ferromagnetic model in a transverse field and uniform long-range interactions among the z components of the spins is studied using the mean-field Jordan–Wigner transformation. The thermodynamic quantities results like Helmholtz free energy, the internal energy, the specific heat and the isothermal susceptibility are obtained both analytically and numerically. The phase transition of the system at a finite temperature is also discussed. Our results agree with numerical results of the XYZ spin chain by others. 相似文献
17.
Anton Bovier Véronique Gayrard Pierre Picco 《Communications in Mathematical Physics》1997,186(2):323-379
We study a one-dimensional version of the Hopfield model with long, but finite range interactions below the critical temperature.
In the thermodynamic limit we obtain large deviation estimates for the distribution of the “local” overlaps, the range of
the interaction, , being the large parameter. We show in particular that the local overlaps in a typical Gibbs configuration are constant and
equal to one of the mean-field equilibrium values on a scale . We also give estimates on the size of typical “jumps”, i.e. the regions where transitions from one equilibrium value to
another take place. Contrary to the situation in the ferromagnetic Kac-model, the structure of the profiles is found to be
governed by the quenched disorder rather than by entropy.
Received: 14 February 1996 / Accepted: 30 September 1996 相似文献
18.
We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero
fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent research interest
and is well understood in the thermodynamic limit. The system shows large finite size effects, and we observe a switching
between metastable fluid and condensed phases close to the critical point, in contrast to the continuous limiting behaviour
of relevant observables. We describe the leading order finite size effects and establish a discontinuity near criticality
in a rigorous scaling limit. We also characterise the metastable phases using a current matching argument and an extension
of the fluid phase to supercritical densities. This constitutes an interesting example where the thermodynamic limit fails
to capture essential parts of the dynamics, which are particularly relevant in applications with moderate system sizes such
as traffic flow or granular clustering. 相似文献
19.
F. Mancini F. P. Mancini 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(3):341-351
Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful
for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard
model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h,
in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional
space (U, n, h) – n is the filling – with relative phase transitions, as well as different types of charge ordering. The magnetic
field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in
the magnetization curves, and a change from a single to a double-peak tructure in the specific heat. According to the value
of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed
study of several thermodynamic quantities is also presented at finite temperature. 相似文献
20.
We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material,contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N →∞.For the finite size,thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain.For the present 1D diatomic chain,obtained value of power divergent exponent of thermal conductivity0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size,increases the thermal conductivity and existence of anomalous energy diffusion.Existing numerical data supports our findings. 相似文献