Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model

2013 ◽  
Vol 14 (2) ◽  
pp. 355-369 ◽  
Author(s):  
J. Kaupužs ◽  
R. V. N. Melnik ◽  
J. Rimšāns
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Specific Heat ◽  
Power Law ◽  
Three Dimensional ◽  
The Other ◽  
Data Sets ◽  
Monte Carlo Data ◽  
Binder Cumulant ◽  
3D Ising Model

AbstractThe singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.

scholarly journals INVESTIGATING THE VOLUME MAXIMIZING THE PROBABILITY OF FINDING ν ELECTRONS FROM VARIATIONAL MONTE CARLO DATA

2005 ◽  
Vol 04 (02) ◽  
pp. 397-409 ◽  
Author(s):  
ANTHONY SCEMAMA
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Particle Density ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Monte Carlo Sampling ◽  
The Other ◽  
Monte Carlo Data ◽  
Variational Monte Carlo ◽  
Three Dimensional Space

An algorithm is introduced for the search of a volume, in the three-dimensional space, which maximizes the probability of finding να up electrons and νβ down electrons inside the volume, all the other electrons being outside of it. This search is performed after a Variational Monte Carlo sampling of the N-particle density generated by the wave function.

scholarly journals Clusters Formed by Dumbbell-like One-Patch Particles Confined in Thin Systems

2021 ◽  
Author(s):  
Masahide Sato
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Particle Interaction ◽  
Three Dimensional ◽  
The Other ◽  
Spherical Particles ◽  
Dimensionless Distance ◽  
Large Island ◽  
Cluster Shape

Abstract Performing isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model. The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between them. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when q < 1. With increasing q, the clusters become chain-like. When q increases further, elongated clusters and regular polygonal clusters are created. In hte simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

scholarly journals Clusters formed by dumbbell-like one-patch particles confined in thin systems

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Masahide Sato
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Particle Interaction ◽  
Three Dimensional ◽  
The Other ◽  
Spherical Particles ◽  
Dimensionless Distance ◽  
Large Island ◽  
Cluster Shape

AbstractPerforming isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model . The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between these centers. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when $$q<1$$ q < 1 . With increasing q, the clusters become chain-like . When q increases further, elongated clusters and regular polygonal clusters are created. In the simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

Monte Carlo Renormalization of the Three-Dimensional Ising Model: The Influence of Truncation

1989 ◽  
Vol 10 (2) ◽  
pp. 105-109 ◽  
Author(s):  
H. W. J Blöte ◽  
J. A. de Bruin ◽  
A Compagner ◽  
J. H Croockewit ◽  
Y. T. J. C Fonk ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Three Dimensional
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