scholarly journals Finite-size scaling of correlation functions in the one-dimensional Anderson-Hubbard model

2010 ◽  
Vol 81 (11) ◽  
Author(s):  
Satoshi Nishimoto ◽  
Tomonori Shirakawa
Keyword(s):  
Hubbard Model ◽  
Correlation Functions ◽  
Finite Size ◽  
Finite Size Scaling ◽  
One Dimensional ◽  
Size Scaling ◽  
The One

Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

2020 ◽  
Vol 75 (2) ◽  
pp. 175-182
Author(s):  
Magdy E. Amin ◽  
Mohamed Moubark ◽  
Yasmin Amin
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Boundary Conditions ◽  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
The One ◽  
Bulk Case

AbstractThe one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

FINITE-SIZE SCALING FOR CELLULAR AUTOMATA WITH RANDOMIZED GRIDS AND FOR FRACTAL RANDOM FIELDS IN DISORDERED SYSTEMS

1996 ◽  
Vol 10 (05) ◽  
pp. 523-542 ◽  
Author(s):  
BIRGITT H. SCHÖNFISCH ◽  
MARCEL OVIDIU VLAD
Keyword(s):  
Cellular Automata ◽  
Size Effect ◽  
Correlation Functions ◽  
Random Distribution ◽  
Concentration Field ◽  
Finite Size ◽  
Finite Size Effect ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Probability Densities

The finite-size effect on the statistics of independent random point processes is analyzed in connection with the theory of cellular automata with randomized grids. The space distribution of a large but finite number N0 of independent particles confined in a large region of ds-dimensional Euclidean space of size VΣ is investigated by using the technique of characteristic functionals. Exact formal expressions are derived for all many-body correlation functions of the positions of the particles as well as for all cumulants of the concentration field. These functions are made up of the contributions of the different negative powers of the total number N0 of particles from the system [Formula: see text] where n =1, 2, … are the orders of the correlation functions or of the cumulants of the concentration field. In the thermodynamic limit N0, VΣ → ∞ with N0 / VΣ = constant only the terms An(0) survive; the other terms An(m) with m > 0 express the finite-size effects. It is shown that, even though the particles are independent, for a finite size of the system a correlation effect different from zero exists among their positions and this correlation vanishes in the limit of an infinite size. The correlation among the positions of the different particles is a finite-size effect due to the conservation of the total number of particles which is similar to the correlation among ideal bosons or fermions at low absolute temperatures. The stochastic properties of an additive scalar field generated by a random distribution of independent particles are investigated. The approach can be applied to the study of stochastic gravitational fluctuations generated by a random distribution of stars or galaxies, of the short-range mean field generated by the particles making up a disordered medium, or of the distribution of the offspring number generated by a plant population randomly distributed in space. Special attention is paid to the finite-size scaling corrections to the long-range self-similar fractal fields. The computations lead to the surprising result that for large values of the resulting field the finite size of the system has practically no influence on the tails of the probability densities of the resulting field, which obey a statistical fractal scaling law of the negative power law type. This apparent paradoxical effect is due to the fact that the very large values of the field corresponding to the tails of the probability densities are generated by the closest neighbor of the test particle considered and are not influenced by the more distant particles.

Fermi surface of the one-dimensional Hubbard model: Finite-size effects

1989 ◽  
Vol 162-164 ◽  
pp. 805-806
Author(s):  
C. Bourbonnais ◽  
H. Nelisse ◽  
A. Reid ◽  
A.-M.S. Tremblay
Keyword(s):  
Fermi Surface ◽  
Hubbard Model ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
One Dimensional ◽  
The One
Sign in / Sign up

Export Citation Format

Share Document