scholarly journals Finding the dominant zero of the energy probability distribution

2021 ◽  
pp. 2150155
Author(s):  
J. J. Carvalho ◽  
A. L. Mota
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Ising Model ◽  
Partition Function ◽  
Probability Distribution ◽  
Processing Time ◽  
Computational Procedure ◽  
Thermodynamic System ◽  
Computer Processing ◽  
Square Lattice

In this work, we present a computational procedure to locate the dominant Fisher zero of the partition function of a thermodynamic system. The procedure greatly reduces the required computer processing time to find the dominant zero when compared to other dominant zero search procedures. As a consequence, when the partition function results in very large polynomials, the accuracy of the results can be increased, since less drastic truncation of the polynomials (or even no truncation) is necessary. We apply the procedure to the 2D Ising model in a square lattice, obtaining very accurate results for the critical temperature and some of the critical exponents of the model. We also show the results obtained when the technique is used with the Monte Carlo simulated 2D Ising model in large lattices.

scholarly journals Critical temperatures of the Ising model on Sierpiñski fractal lattices

2020 ◽  
Vol 244 ◽  
pp. 01013
Author(s):  
Michel Perreau
Keyword(s):  
Fractal Dimension ◽  
Critical Temperature ◽  
Ising Model ◽  
Partition Function ◽  
Fractal Dimensions ◽  
Simple Expression ◽  
Square Lattice ◽  
Critical Temperatures ◽  
Wide Range ◽  
Sierpinski Carpets

We report our latest results of the spectra and critical temperatures of the partition function of the Ising model on deterministic Sierpiñski carpets in a wide range of fractal dimensions. Several examples of spectra are given. When the fractal dimension increases (and correlatively the lacunarity decreases), the spectra aggregates more and more tightly along the spectrum of the regular square lattice. The single real root vc, comprised between 0 and 1, of the partition function, which corresponds to the critical temperature Tc through the formula vc = tanh(1/Tc), reliably fits a power law of exponent k where k is the segmentation step of the fractal structure. This simple expression allows to extrapolate the critical temperature for k → ∞. The plot of the logarithm of this extrapolated critical temperature versus the fractal dimension appears to be reliably linear in a wide range of fractal dimensions, except for highly lacunary structures of fractal dimensions close from 1 (the dimension of a quasilinear lattice) where the critical temperature goes to 0 and its logarithm to −∞.

A CORRELATION BETWEEN PERCOLATION MODEL AND ISING MODEL

1996 ◽  
Vol 07 (04) ◽  
pp. 609-612 ◽  
Author(s):  
R. HACKL ◽  
I. MORGENSTERN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Percolation Threshold ◽  
Higher Dimensions ◽  
Percolation Model ◽  
Critical Values ◽  
Square Lattice ◽  
Approximation Formula ◽  
Two Dimensional

In this article we will expose a connection between critical values of percolation and Ising model, i.e., the percolation threshold pc, and the critical temperature Tc and energy Ec, respectively, by the approximation [Formula: see text]. For the two-dimensional square lattice even the identity holds. For higher dimensions — up to d = 7 — and other lattice types we find remarkably small differences from one to five percent.

SHORT TIME CORRELATIONS IN A TWO-DIMENSIONAL ISING MODEL WITH A LINE OF DEFECTS

2001 ◽  
Vol 15 (25) ◽  
pp. 1141-1146 ◽  
Author(s):  
T. TOMÉ ◽  
C. S. SIMÕES ◽  
J. R. DRUGOWICH DE FELÍCIO
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Ising Model ◽  
Early Time ◽  
Time Correlation ◽  
Two Dimensional ◽  
Time Dynamics ◽  
Time Correlations ◽  
Time Regime ◽  
Short Time

We study the short time dynamics of a two-dimensional Ising model with a line of defects. The dynamical critical exponent θ associated to the early time regime at the critical temperature was obtained by Monte Carlo simulations. The exponent θ was estimated by a method where the quantity of interest is the time correlation of the magnetization.

Phase Transition in 2D Anisotropic Ising Model with Next-Nearest Neighbor Interactions in a Magnetic Field

SPIN ◽  
2018 ◽  
Vol 08 (03) ◽  
pp. 1850010
Author(s):  
D. Farsal ◽  
M. Badia ◽  
M. Bennai
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo ◽  
Magnetic Susceptibility ◽  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
The Magnetic Field

The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.

Monte Carlo study of the change of critical temperature in a diluted Ising model due to configuration disorder

2007 ◽  
Vol 360 (3) ◽  
pp. 411-414 ◽  
Author(s):  
W.R. Aguirre-Contreras ◽  
Ligia E. Zamora ◽  
G. Pérez Alcázar ◽  
J.A. Plascak ◽  
J. Restrepo
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Ising Model ◽  
Monte Carlo Study
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