Applicability of Ising model on real materials

In summary, the conversation discusses the speaker's choice of a Monte Carlo simulation for their Computational Physics project and their difficulty in formulating the exact problem. They mention that the Ising model is often used as a toy model in simulations and that introducing a third dimension may be challenging. The speaker also asks about materials that can be described by the Ising model or the Heisenberg model. Finally, they mention that a programming time of 30-50 hours is expected and suggest the application of the Ising model to the adsorption of H on Pd as a potential project.
  • #1
guest1234
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1
Hi

I chose a Monte Carlo simulation of the 2D Ising model as my Computational Physics course project. Unfortunately, I ran intro problems when formulating the exact problem since my professor probably wants me to simulate a real life material and extract magnetization curve M(T,H) out of it. After doing some superficial research on the topic it has occurred to me that 2D Ising model presented in most MC textbooks is just a toy model/framework that is extended and/or modified according to needs. Physical quantities parametrizing simulations in most examples are just dimensionless ratios..

Problem probably still remains when to introduce naively a third dimension (making lattice primitive cubic). Implementing a fcc/bcc type of lattice in 3D seems quite nontrivial (a custom underlying data structure is needed, plain arrays won't suffice).

Is there any materials whose magnetic properties can be described by 2D/3D Ising model? What about Heisenberg model?

To put things in perspective, 30-50h of programming is expected.
 
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  • #2

1. What is the Ising model?

The Ising model is a mathematical model used to describe the behavior of interacting particles in a system, such as atoms in a magnet. It was first proposed by physicist Ernst Ising in the 1920s as a simplified model for studying phase transitions in materials.

2. How does the Ising model apply to real materials?

The Ising model can be applied to real materials by considering the interactions between individual particles and their neighboring particles. These interactions can be described using mathematical equations, and the resulting patterns of spins can be used to predict the behavior of the material.

3. What are the limitations of the Ising model?

The Ising model is a simplified model and does not account for all of the complexities of real materials. For example, it does not take into account the effects of temperature, external fields, or the three-dimensional nature of most materials. It also assumes that all interactions between particles are equal, which may not be the case in some materials.

4. Can the Ising model accurately predict the behavior of real materials?

The Ising model can provide useful insights into the behavior of real materials, but it is not always accurate. Its predictions may be less accurate for materials with more complex structures or for systems that are far from equilibrium. It is important to use caution when applying the Ising model to real materials and to consider its limitations.

5. What are some examples of real materials that can be described using the Ising model?

The Ising model has been applied to a wide range of materials, including ferromagnets, anti-ferromagnets, and spin glasses. It has also been used to study phase transitions in liquid crystals, binary alloys, and biological systems such as protein folding. In general, any material with interacting particles can potentially be described using the Ising model.

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