A Monte Carlo simulation of steady state of 2D Ising model in temperature field

2016 ◽  
Vol 30 (04) ◽  
pp. 1650022 ◽  
Author(s):  
Zeshun Chen ◽  
Changming Xiao ◽  
Zhen Yao
Keyword(s):  
Monte Carlo ◽  
Temperature Field ◽  
Steady State ◽  
Ising Model ◽  
Low Temperatures ◽  
Ferromagnetic State ◽  
Model System ◽  
Local Magnetization ◽  
New Energy ◽  
High And Low Temperatures

Supposing the Ising model system is placed in a temperature field with constant high and low temperatures on both sides, then the system will shift to a non-equilibrium steady state with a certain temperature gradient. With the assistance of local temperature, the steady state of two-dimensional Ising model is studied via the avenue of Monte Carlo simulations in this paper. It is found that the local energy and magnetization are continuous, but there is a sharp decline in the magnetization strength when the temperature falls into the range of 2.2–2.4. The local magnetization [Formula: see text], when the temperature [Formula: see text]. It is the indication that the system is in the ferromagnetic state. However, when [Formula: see text], [Formula: see text], and then the ferromagnetic state turns into the paramagnetic state. Furthermore, a completely new and special state of Ising model system and the corresponding material is possible if the high and low temperatures of the temperature field are larger and smaller than the critical value of the system, respectively. According to this material, the magnetic driving machine, from which a new energy source can be obtained, is qualitatively discussed at the end of this paper.

INTERFACE TENSIONS OF BINARY SYSTEMS

1992 ◽  
Vol 03 (05) ◽  
pp. 879-887 ◽  
Author(s):  
GERNOT MÜNSTER
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Low Temperatures ◽  
Binary Systems ◽  
Three Dimensional ◽  
Liquid Mixtures ◽  
Interface Tension ◽  
Monte Carlo Calculations ◽  
Pure Phases ◽  
Semiclassical Expansion

In liquid mixtures or analogous binary systems at low temperatures the pure phases may coexist, separated by an interface. The interface tension vanishes according to σ=σ0(1−T/Tc)µ as the temperature T approaches the critical point from below. Similarly the correlation length diverges as ξ=ξ0(T/Tc−1)−ν. For three-dimensional systems the dimensionless product R=σ0(ξ0)2 is universal. This and related universal quantities are investigated by means of a semiclassical expansion in the framework of Φ4 theory, as well as by Monte Carlo calculations in the three-dimensional Ising model.

Studying on effective local region size of Ising model in non-equilibrium steady state

2019 ◽  
Vol 33 (02) ◽  
pp. 1950005
Author(s):  
Yuanxiang Deng ◽  
Changming Xiao
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Ising Model ◽  
Large Scale ◽  
Local Region ◽  
Two Dimensional ◽  
Calculation Results ◽  
The Difference ◽  
Region Size ◽  
Non Equilibrium

In this paper, both the local region and sub-Monte Carlo steps were introduced to study the non-equilibrium steady state of two-dimensional Ising model. As the size of local region can vary on a large scale, it is very important to determine the effective local region size. In our studies, a series of local regions with different sizes were taken into consideration, and the results show that, when the temperature of a local region is far away from the critical temperature of the system, no matter the local region size is large or small, the results obtained by our calculations are almost the same; however, when the temperature of the local region is near to the critical point, the difference between the calculated results is very large if the local region size is very small, but this difference will decrease quickly when the local region size is enlarged, and the calculation results will tend to be the same when the local region size is larger than a certain value. Furthermore, the numerical results show that the effective local region size is almost unaffected by the temperature gradient of the system. It is clear that the local region and expanded Monte Carlo method provide us an efficient numerical method to study the non-equilibrium steady state.

scholarly journals Neutronics for the GEMINI+ HTGR

2021 ◽  
Vol 2048 (1) ◽  
pp. 012030
Author(s):  
J C Kuijper ◽  
D Muszynski
Keyword(s):  
Monte Carlo ◽  
Temperature Field ◽  
Steady State ◽  
Temperature Distribution ◽  
The Netherlands ◽  
Particle Transport ◽  
Data Exchange ◽  
Horizon 2020 ◽  
The Core ◽  
Design Calculations

Abstract Literally at the heart of the Euratom Horizon 2020 project GEMINI+ are the core neutronics (design) calculations. For these calculations on a relatively small (180 MWth) prismatic HTGR with cylindrical core, the 3-D monte-carlo particle transport and depletion code SERPENT version 2 (VTT, Finland) was selected, the main reasons being the flexibility and versatility of this code. This enables the modelling of all relevant details of the reactor without unnecessary approximations. A particularly useful feature of the SERPENT code is the multiphysics input capability. This allows to map a temperature field over the defined geometry, enabling the calculation of converged power and temperature distribution by means of iteration and data exchange between SERPENT and a (steady-state) thermal- hydraulics code. In this particular case the SPECTRA code (NRG, The Netherlands) was used to provide the temperature distribution. 4 to 5 iterations are sufficient to reach simultaneously converged distributions for power and temperature. The paper gives an overview of the performed analyses for the current (June 2020) design of the GEMINI+ HTGR, and results thereof. Neutronics features seem quite promising, but further improvements and therefore further investigations would be desirable.

Simple Systems

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Magnetic Field ◽  
Low Temperatures ◽  
General Framework ◽  
Gibbs State ◽  
Macroscopic System ◽  
Basic Model ◽  
System A ◽  
Paramagnetic Salt ◽  
High And Low Temperatures ◽  
Simple Systems

Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic oscillator, a rotor, and a spin in a magnetic field. These applications serve to illustrate how a key function associated with the Gibbs state, the so-called partition function, is calculated in practice, how the entropy function is obtained via a Legendre transformation, and how such systems behave in the limits of high and low temperatures. After discussing these simple systems, this chapter considers a first example where multiple constituents are assembled into a macroscopic system: a basic model of a paramagnetic salt. It also investigates the size of energy fluctuations and how—in the case of the paramagnet—these fluctuations scale with the number of constituents.

Should a hotter paramagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model

2021 ◽  
Author(s):  
Subir K Das ◽  
Nalina Vadakkayil
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Simulation Results ◽  
Heating Up

For quicker formation of ice, before inserting inside a refrigerator, heating up of a body of water can be beneficial. We report first observation of a counterpart of this intriguing...

scholarly journals The Ising model with Hybrid Monte Carlo

2021 ◽  
Vol 265 ◽  
pp. 107978
Author(s):  
Johann Ostmeyer ◽  
Evan Berkowitz ◽  
Thomas Luu ◽  
Marcus Petschlies ◽  
Ferenc Pittler
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Hybrid Monte Carlo
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