Ising-Model Critical Indices below the Critical Temperature

1967 ◽  
Vol 155 (2) ◽  
pp. 545-552 ◽  
Author(s):  
George A. Baker ◽  
David S. Gaunt
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Critical Indices

Logarithmic Factors, Critical Temperature, and Zero Temperature Flipping in the 4D Kinetic Ising Model

1997 ◽  
Vol 08 (02) ◽  
pp. 263-267 ◽  
Author(s):  
Dietrich Stauffer ◽  
Joan Adler
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Kinetic Monte Carlo ◽  
Series Expansions ◽  
Fourth Moment ◽  
Zero Temperature ◽  
Kinetic Ising Model ◽  
Kinetic Monte Carlo Simulations ◽  
Error Bars

We determine the critical temperature in the four-dimensional nearest-neighbor Ising model as J/kB Tc=0.149694±0.000002 from kinetic Monte Carlo simulations of up to 5764 spins. Here we assume the critical magnetization to decay with time as (t/ log t)-1/2. However, possible logarithmic additions to this leading scaling behavior could change the estimate beyond these error bars. A reanalyzis of old series expansions for the susceptibility and fourth moment gives 0.149696±0.000004.

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.

scholarly journals CONSTRUCTING THE CRITICAL CURVE FOR A SYMMETRIC TWO-LAYER ISING MODEL

2004 ◽  
Vol 03 (02) ◽  
pp. 217-224 ◽  
Author(s):  
M. GHAEMI ◽  
B. MIRZA ◽  
G. A. PARSAFAR
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Numerical Method ◽  
Critical Points ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Nearest Neighbor ◽  
Neighbor Interaction ◽  
Ising Ferromagnet ◽  
Shift Exponent

A numerical method based on the transfer matrix method is developed to calculate the critical temperature of two-layer Ising ferromagnet with a weak inter-layer coupling. The reduced internal energy per site has been accurately calculated for symmetric ferromagnetic case, with the nearest neighbor coupling K1=K2=K (where K1 and K2 are the nearest neighbor interaction in the first and second layers, respectively) with inter-layer coupling J. The critical temperature as a function of the inter-layer coupling [Formula: see text], is obtained for very weak inter-layer interactions, ξ<0.1. Also a different function is given for the case of the strong inter-layer interactions (ξ>1). The importance of these relations is due to the fact that there is no well tabulated data for the critical points versus J/K. We find the value of the shift exponent ϕ=γ is 1.74 for the system with the same intra-layer interaction and 0.5 for the system with different intra-layer interactions.

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.

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