Finite-size effects on a lattice calculation

We study in this Letter the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.     

Finite-size effects in a cellular automaton for diffusion

The question whether diffusion in the hard-square lattice gas is blocked in the thermodynamic limit is mapped to the problem whether percolation occurs in the time evolution of a cellular automaton. The final states of the cellular automaton are investigated for varying lattice sizes from 6×6 up to 20,035×20,032. The results seem to indicate that there is a percolation threshold, i.e., a range of concentrations for which diffusion is blocked. However, since this cannot be true for the infinite system, as proven rigorously, it is concluded that finite-size effects persist for this system up to very large sizes.     

Finite-size effects on nucleation in a first-order phase transition

We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark–gluon plasma generated in high-energy heavy ion collisions. Very general arguments allow us to show that the finite size of the early universe has virtually no relevance in the process of nucleation and in the growth of cosmological bubbles during the primordial quark–hadron and the electroweak phase transitions. In the case of high-energy heavy ion collisions, finite-size effects play an important role in the late-stage growth of hadronic bubbles.     

Finite-size effects at first-order transitions

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=T_c.     

理想量子气体的尺度效应

根据欧拉-麦克劳林(Euler-MacLaurin)公式,导出有限理想量子气体的热力学量表达式,揭示系统尺度和边界形状对其性质的影响.结果表明,有限尺度效应导致了一系列与热力学极限条件下不同的性质特征,如系统的非广延性和压强的各向异性等.     

Finite-size effects in a field-theoretic model with long-range exchange interaction

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/r ^d+2–2,0⁺,0⁺. Renormalization group calculations ind=d _u – are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.     

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula,this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container.The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed.It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy.It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects,such as the nonextensivity of the system,the anisotropy of the pressure,and so on.     

Magnetic field effects on a classical anisotropic spin-glass model

The simple model of a classical spin-glass proposed by van Hemmen [1] is extended to the case of a generalS Ising spin and anisotropy energy. Due to its simplicity, the model is amenable to an exact solution and in the case of spin-1 the phase diagram is similar to that of the Sherrington-Kirkpatrick model. ForS=1 and for certain values of the anisotropy the phase diagram in the (H-T) plane shows continuous and discontinuous transitions, a critical point within the condensed phase, and a field-induced mixed phase in addition to the paramagnetic and spin-glass phases.Work partially supported by CNPq and FINEP (Brazilian Agencies). Part of this work was presented at the International Conference of Magnetism, San Francisco, 1985     

Finite-size effects in conductance measurements on quantum dots

The observation of the Kondo effect in quantum dots has provided new opportunities to finally observe the controversial Kondo screening cloud. Here we study the conductance of a quantum dot embedded in a finite length quantum wire, predicting a change in behavior when the length of the wire is comparable to the size of the screening cloud.     

Finite-size effects on intensity correlations in random media

The correlations between waves transmitted through random media are analyzed by use of a random-matrix approach and numerical simulations of rough waveguides. Although the intensity and conductance fluctuations are practically independent of the sample length, the correlations present a strong dependence on the length of the disordered region. In waveguide geometries the long-range correlations C((2)) and C((3)), usually associated to intensity and conductance fluctuations, respectively, become negative as the length of the system decreases. Our results provide a new interpretation of recent optical experiments on disordered slab geometries.     

Finite-size effects in the self-organized critical forest-fire model

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in conventional critical systems. Rather, the system is composed of relatively homogeneous patches of different tree densities, leading to two qualitatively different types of fires: those that span an entire patch and those that do not. As the system size becomes smaller, the system contains less patches, and finally becomes homogeneous, with large density fluctuations in time. Received 24 April 1999 and Received in final form 26 October 1999     

Finite-size effects in tunneling between parallel quantum wires

We present theoretical calculations and experimental measurements which reveal finite-size effects in the tunneling between two parallel quantum wires, fabricated at the cleaved edge of a GaAs/AlGaAs bilayer heterostructure. Observed oscillations in the differential conductance, as a function of bias voltage and applied magnetic field, provide direct information on the shape of the confining potential. Superimposed modulations indicate the existence of two distinct excitation velocities, as expected from spin-charge separation.     

Finite-size effects for some bootstrap percolation models

The consequences of Schonmann's new proof that the critical threshold is unity for certain bootstrap percolation models are explored. It is shown that this proof provides an upper bound for the finite-size scaling in these systems. Comparison with data for one case demonstrates that this scaling appears to give the correct asymptotics. We show that the threshold for a finite system of sizeL scales asO[ln(lnL)] for the isotropic model in three dimensions where sites that fail to have at least four neighbors are culled.Related systems have been studied in the context of cellular automata.⁽⁴⁾     

Finite-size effects of a left-handed material slab on the image quality

The characteristics of an imaging system formed by a left-handed material (LHM) slab of finite length are studied, and the influence of the finite length of the slab on the image quality is analyzed. Unusual phenomena such as surface bright spots and negative energy stream at the image side are observed and explained as the cavity effects of surface plasmons excited by the evanescent components of the incident field. For a thin LHM slab, the cavity effects are found rather sensitive to the length of the slab; the bright spots on the bottom surface of the slab may stretch to the image plane and degrade the image quality.