scholarly journals Phase diagram of an Ising model for ultrathin magnetic films: Comparing mean field and Monte Carlo predictions

2007 ◽  
Vol 75 (22) ◽  
Author(s):  
Santiago A. Pighín ◽  
Sergio A. Cannas
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Ising Model ◽  
Mean Field ◽  
Magnetic Films

DYNAMICAL CRITICAL BEHAVIOR OF THE FOUR-DIMENSIONAL ISING MODEL

1996 ◽  
Vol 06 (06) ◽  
pp. 807-812 ◽  
Author(s):  
JOAN ADLER ◽  
DIETRICH STAUFFER
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Mean Field ◽  
Glauber Dynamics ◽  
Series Analysis ◽  
Logarithmic Corrections ◽  
Field Behavior

Monte Carlo simulations of the Glauber dynamics in the four-dimensional Ising model with up to 3124 spins agree with the theoretically expected logarithmic corrections to mean field behavior, if we assume J/kBTc = 0.14970, consistent with some series analysis.

ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A JUNCTION: THE EFFECT OF UNEQUAL INJECTION RATES

2009 ◽  
Vol 20 (06) ◽  
pp. 967-978 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
KATSUHIRO NISHINARI ◽  
MAO-BIN HU ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Exclusion Processes ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Injection Rates

Asymmetric exclusion processes (ASEP) on lattices with a junction, in which two or more parallel lattice branches combine into a single one, is important as a model for complex transport phenomena. This paper investigates the effect of unequal injection rates in ASEP with a junction. It is a generalization of the work of Pronina and Kolomeisky [J. Stat. Mech. P07010 (2005)], in which only equal injection rates are considered. It is shown that the unequal rates give rise to new phases and the phase diagram structure is qualitatively changed. The phase diagram and the density profiles are investigated by using Monte Carlo simulations, mean field approximation and domain wall approach. The analytical results are in good agreement with Monte Carlo simulations.

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.

Phase Diagram and Orientational Order of a System with Second and Fourth Rank Interactions

1997 ◽  
Vol 11 (16) ◽  
pp. 1937-1944 ◽  
Author(s):  
Cesare Chiccoli ◽  
Paolo Pasini ◽  
Claudio Zannoni
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Liquid Crystals ◽  
Computer Simulations ◽  
Order Parameter ◽  
Orientational Order ◽  
Mean Field ◽  
Rank One ◽  
Site Cluster ◽  
Typical Temperature

A simple generalized Lebwohl–Lasher model for liquid crystals, where a fourth rank interaction is added to the usual second rank one, is investigated in detail. We have obtained the phase diagram of the system performing extensive Monte Carlo computer simulations for a range of the fourth to the second rank relative strengths and we compare it with the prediction of Mean Field and Two Site Cluster theories. We show that the addition of a non-negligible fourth rank term significantly changes the temperature dependence of the order parameter. Fourth rank contributions larger than 20% worsen the agreement of the model with the typical temperature behavior of the order in nematics.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

scholarly journals Investigation of Multicritical Phenomena in ANNNI Model by Monte Carlo Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-4
Author(s):  
A. K. Murtazaev ◽  
J. G. Ibaev
Keyword(s):  
Phase Diagram ◽  
Heat Capacity ◽  
Monte Carlo ◽  
Ising Model ◽  
Wide Temperature Range ◽  
Monte Carlo Methods ◽  
Correlation Radius ◽  
Competing Interactions ◽  
Annni Model ◽  
Lifshitz Point

The anisotropic Ising model with competing interactions is investigated in wide temperature range and |J1/J| parameters by means of Monte Carlo methods. Static critical exponents of the magnetization, susceptibility, heat capacity, and correlation radius are calculated in the neighborhood of Lifshitz point. According to obtained results, a phase diagram is plotted, the coordinates of Lifshitz point are defined, and a character of multicritical behavior of the system is detected.

TOTALLY ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A BRANCHING POINT

2009 ◽  
Vol 20 (12) ◽  
pp. 1999-2012 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
MAO-BIN HU ◽  
KATSUHIRO NISHINARI ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Exclusion Process ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Single Chain ◽  
Equal Rate ◽  
Branching Point

We study totally asymmetric simple exclusion process (TASEP) where particles move on a single-chain lattice which diverges into two parallel lattice branches. At the branching point, the particles move to one of the two branches with equal rate r/2. The phase diagram and density profiles are investigated by using mean-field approximation and Monte Carlo simulations. It is found that the phase diagram can be classified into three regions at any value of r. However, a threshold [Formula: see text] is identified. In cases of r > rc and r < rc, the phase diagram exhibits qualitatively different phases. The analytical results are in good agreement with the results of Monte Carlo simulations.

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