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.

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.

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.

PAIRWISE ENTANGLEMENT IN THE N-QUBIT XX MODEL WITH DZYALOSHINSKI–MORIYA INTERACTION AND MAGNETIC FIELD

2011 ◽  
Vol 25 (16) ◽  
pp. 2135-2148
Author(s):  
BIN ZHOU
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
Magnetic Fields ◽  
Nearest Neighbor ◽  
Zero Temperature ◽  
Thermal Entanglement ◽  
Dm Interaction ◽  
Xx Model ◽  
Moriya Interaction

In this paper, we investigate the role of Dzyaloshinski–Moriya (DM) interaction in the pairwise entanglement in the three- and four-qubit XX models with magnetic field. In the four-qubit model, the pairwise entanglements of two nearest-neighbor qubits and two next-neighbor qubits are investigated, respectively. The dependences of the critical temperature at which the pairwise thermal entanglement disappears on DM interaction and magnetic fields are studied in details. At zero temperature, the entanglement can undergo sudden changes with adjustment of the parameters, and the general results of the concurrence are obtained in all cases.

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4911-4917
Author(s):  
YEE MOU KAO ◽  
MALL CHEN ◽  
KEH YING LIN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Spontaneous Magnetization ◽  
Temperature Series ◽  
Square Lattice ◽  
Series Expansions ◽  
Zero Field ◽  
Ferromagnetic Ising Model ◽  
Neighbour Interaction

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

Mound Formation and Coarsening in Homoepitaxial Growth

1996 ◽  
Vol 440 ◽  
Author(s):  
Jacques G. Amar ◽  
Fereydoon Family
Keyword(s):  
Critical Temperature ◽  
Kinetic Monte Carlo ◽  
Layer Growth ◽  
Layer By Layer ◽  
Island Nucleation ◽  
Homoepitaxial Growth ◽  
Kinetic Monte Carlo Simulations ◽  
Temperature Deposition ◽  
Mound Formation ◽  
Positive Step

AbstractThe effects of instabilities which lead to mound formation and coarsening in homoepitaxial growth on metal (100) surfaces are discussed. These include an instability due to the Ehrlich-Schwoebel step barrier to interlayer diffusion as well as an instability due to step-adatom attraction at ascending steps. A unified picture of the effects of attractive and repulsive interactions at ascending and descending steps on surface morphology and island nucleation is presented. An analytic calculation of the selected mound angle and critical temperature for mound formation as a function of both the Ehrlich-Schwoebel step barrier and the barrier to diffusion towards an ascending step is also presented. Depending on the sign of the step barrier and the magnitude of the prefactor for diffusion over a step various scenarios are possible, including the existence of a critical temperature for mound formation above which (for a positive step barrier) or below which (for a negative step barrier) quasi-layer-by-layer growth will be observed. A theoretical analysis also leads to an accurate prediction of the observed mound angle for Fe/Fe(100) deposition at room temperature. The general dependence of the mound angle, surface skewness, and mound coarsening exponent on temperature, deposition rate, and strength of the step barrier is also studied via kinetic Monte Carlo simulations of bcc(100) growth and compared with recent experiments.

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