Finite-size effects in exponential random graphs

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
A Gorsky ◽  
O Valba
Keyword(s):  
Random Graphs ◽  
Ground State ◽  
Size Effects ◽  
Chemical Potential ◽  
Network Flows ◽  
Finite Size ◽  
Critical Value ◽  
Star Model ◽  
Finite Size Effects ◽  
Exponential Random Graphs

Abstract In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density $p<0.5$ or as the single cluster at $p>0.5$. We find that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover. At $N>N^{*}(p),$ the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at $N>N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.

scholarly journals Finite size effects in the Gross-Neveu model with isospin chemical potential

2008 ◽  
Vol 78 (4) ◽  
Author(s):  
D. Ebert ◽  
K. G. Klimenko ◽  
A. V. Tyukov ◽  
V. Ch. Zhukovsky
Keyword(s):  
Size Effects ◽  
Chemical Potential ◽  
Finite Size ◽  
Finite Size Effects ◽  
Gross Neveu Model

scholarly journals Homogeneous one-dimensional Bose–Einstein condensate in the Bogoliubov’s regime

2016 ◽  
Vol 30 (22) ◽  
pp. 1650307 ◽  
Author(s):  
Elías Castellanos
Keyword(s):  
Ground State ◽  
Size Effects ◽  
Finite Size ◽  
Einstein Condensate ◽  
Finite Size Effects ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Ground State Properties ◽  
Low Dimensional ◽  
Bose Einstein

We analyze the corrections caused by finite size effects upon the ground state properties of a homogeneous one-dimensional (1D) Bose–Einstein condensate. We assume from the very beginning that the Bogoliubov’s formalism is valid and consequently, we show that in order to obtain a well-defined ground state properties, finite size effects of the system must be taken into account. Indeed, the formalism described in the present paper allows to recover the usual properties related to the ground state of a homogeneous 1D Bose–Einstein condensate but corrected by finite size effects of the system. Finally, this scenario allows us to analyze the sensitivity of the system when the Bogoliubov’s regime is valid and when finite size effects are present. These facts open the possibility to apply these ideas to more realistic scenarios, e.g. low-dimensional trapped Bose–Einstein condensates.

scholarly journals Finite size effects for the Ising model on random graphs with varying dilution

2009 ◽  
Vol 388 (17) ◽  
pp. 3413-3425 ◽  
Author(s):  
Julien Barré ◽  
Antonia Ciani ◽  
Duccio Fanelli ◽  
Franco Bagnoli ◽  
Stefano Ruffo
Keyword(s):  
Ising Model ◽  
Random Graphs ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects

scholarly journals FINITE SIZE EFFECTS IN ENTANGLED RINGS OF QUBITS

2004 ◽  
Vol 02 (02) ◽  
pp. 149-169 ◽  
Author(s):  
T. MEYER ◽  
U. V. POULSEN ◽  
K. ECKERT ◽  
M. LEWENSTEIN ◽  
D. BRUß
Keyword(s):  
Ground State ◽  
Size Effects ◽  
State Energy ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Nearest Neighbors ◽  
Spin Model ◽  
Total Spin ◽  
Finite Size Effects ◽  
Invariant Rings

We study translationally invariant rings of qubits with a finite number of sites N, and determine the maximal nearest-neighbor entanglement for a fixed z-component of the total spin. For small numbers of sites we present analytical results. We establish a relation between the maximal nearest-neighbor concurrence and the ground state energy of an XXZ spin model. This connection allows us to calculate the concurrence numerically for N≤24. We point out some interesting finite-size effects. Finally, we generalize our results beyond nearest neighbors.

scholarly journals STABILITY OF COLOR-FLAVOR LOCKED STRANGELETS

2006 ◽  
Vol 21 (13n14) ◽  
pp. 3021-3030 ◽  
Author(s):  
O. KIRIYAMA
Keyword(s):  
Size Effects ◽  
Thermodynamic Potential ◽  
Finite Size ◽  
Baryon Number ◽  
Critical Value ◽  
Coupling Constant ◽  
Finite Size Effects ◽  
Quark Coupling ◽  
The Stability ◽  
Quark Flavors

The stability of color-flavor locked (CFL) strangelets is studied in the three-flavor Nambu–Jona-Lasinio model. We consider all quark flavors to be massless, for simplicity. By making use of the multiple reflection expansion, we explicitly take into account finite size effects and formulate the thermodynamic potential for CFL strangelets. We find that the CFL gap could be large enough so that the energy per baryon number of CFL strangelets is greatly affected. In addition, if the quark–quark coupling constant is larger than a certain critical value, there is a possibility of finding absolutely stable CFL strangelets.

scholarly journals Unzipping of two random heteropolymers: Ground-state energy and finite-size effects

2008 ◽  
Vol 78 (1) ◽  
Author(s):  
M. V. Tamm ◽  
S. K. Nechaev
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Size Effects ◽  
State Energy ◽  
Finite Size ◽  
Finite Size Effects

scholarly journals Finite size effects in the presence of a chemical potential: A study in the classical nonlinearO(2)sigma model

2010 ◽  
Vol 81 (12) ◽  
Author(s):  
Debasish Banerjee ◽  
Shailesh Chandrasekharan
Keyword(s):  
Size Effects ◽  
Sigma Model ◽  
Chemical Potential ◽  
Finite Size ◽  
Finite Size Effects

Using polymer films to probe finite size effects in glass forming materials

2000 ◽  
Vol 10 (PR7) ◽  
pp. Pr7-251-Pr7-254 ◽  
Author(s):  
J. A. Forrest ◽  
J. Mattsson
Keyword(s):  
Polymer Films ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
Glass Forming ◽  
Glass Forming Materials
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