scholarly journals PERSISTENCE IN THE ZERO-TEMPERATURE DYNAMICS OF THE Q-STATES POTTS MODEL ON UNDIRECTED-DIRECTED BARABÁSI–ALBERT NETWORKS AND ERDÖS–RÉNYI RANDOM GRAPHS

2008 ◽  
Vol 19 (12) ◽  
pp. 1777-1785 ◽  
Author(s):  
F. P. FERNANDES ◽  
F. W. S. LIMA
Keyword(s):  
Random Graphs ◽  
Potts Model ◽  
Finite Size ◽  
Glauber Dynamics ◽  
The Other ◽  
Finite Size Effect ◽  
Zero Temperature ◽  
Temperature Dynamics ◽  
Short Times ◽  
Q Values

The zero-temperature Glauber dynamics is used to investigate the persistence probability P(t) in the Potts model with Q = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16 384, …, 230 states on directed and undirected Barabási–Albert networks and Erdös–Rényi (ER) random graphs. In this model, it is found that P(t) decays exponentially to zero in short times for directed and undirected ER random graphs. For directed and undirected BA networks, in contrast it decays exponentially to a constant value for long times, i.e., P(∞) is different from zero for all Q values (here studied) from Q = 3, 4, 5, …, 230; this shows "blocking" for all these Q values. Except that for Q = 230 in the undirected case P(t) tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

On The Phase Structure of the Asymmetric Three-State Potts Model

1982 ◽  
Vol 21 ◽  
Author(s):  
G. v. Gehlen
Keyword(s):  
Phase Boundary ◽  
Potts Model ◽  
Phase Structure ◽  
Asymmetry Parameter ◽  
Finite Size ◽  
Critical Index ◽  
Incommensurate Phase ◽  
Finite Size Scaling ◽  
Lifshitz Point ◽  
The Asymmetry

ABSTRACTFinite-size scaling is applied to the Hamiltonian version of the asymmetric Z3-Potts model. Results for the phase boundary of the commensurate region and for the corresponding critical index ν are presented. It is argued that there is no Lifshitz point, the incommensurate phase extending down to small values of the asymmetry parameter.

scholarly journals Theoretical Investigation of the Size Effect on the Oxygen Adsorption Energy of Coinage Metal Nanoparticles

2021 ◽  
Author(s):  
Amir H. Hakimioun ◽  
Elisabeth M. Dietze ◽  
Bart D. Vandegehuchte ◽  
Daniel Curulla-Ferre ◽  
Lennart Joos ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Effect ◽  
Adsorption Energy ◽  
Single Point ◽  
Finite Size ◽  
Geometry Optimization ◽  
Oxygen Adsorption ◽  
Finite Size Effect ◽  
Full Geometry Optimization ◽  
Coinage Metal

AbstractThis study evaluates the finite size effect on the oxygen adsorption energy of coinage metal (Cu, Ag and Au) cuboctahedral nanoparticles in the size range of 13 to 1415 atoms (0.7–3.5 nm in diameter). Trends in particle size effects are well described with single point calculations, in which the metal atoms are frozen in their bulk position and the oxygen atom is added in a location determined from periodic surface calculations. This is shown explicitly for Cu nanoparticles, for which full geometry optimization only leads to a constant offset between relaxed and unrelaxed adsorption energies that is independent of particle size. With increasing cluster size, the adsorption energy converges systematically to the limit of the (211) extended surface. The 55-atomic cluster is an outlier for all of the coinage metals and all three materials show similar behavior with respect to particle size. Graphic Abstract

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