Where Can I Find Exact Results for the Ising Model?

In summary, the Ising model is a mathematical model used to study the behavior of interacting particles in a system. It represents a system as a lattice of discrete points with binary states, and uses probabilistic equations to determine the likelihood of spin flips. Exact results on the Ising model refer to mathematical solutions that provide precise values for key properties, allowing for a deeper understanding and serving as a benchmark for other methods. Current research on exact results includes higher-dimensional lattices, the effect of disorder, and application to other fields.
  • #1
wdlang
307
0
is there any reference on ising model

i would like to see all the exact results on ising model

for 2d ising model, the correlation length diverge as t to -1 around the critical temperature

how is this result derived?
 
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  • #2
Take a look at the book by Baxter, https://www.amazon.com/dp/0486462714/?tag=pfamazon01-20. It solves the 1d and 2d Ising models exactly, as well as many other statistical mechanical models. Be warned, though, the solutions are quite involved for most of these models! (Also, there are no exactly solved 3d models, in case you were wondering).
 
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FAQ: Where Can I Find Exact Results for the Ising Model?

What is the Ising model?

The Ising model is a mathematical model used in statistical mechanics to study the behavior of interacting particles in a system. It was originally developed to understand the behavior of magnetic materials, but has since been applied to a variety of systems, including social networks and biological systems.

How does the Ising model work?

The Ising model represents a system as a lattice of discrete points, with each point having a binary state (spin) of either up or down. The model uses probabilistic equations to determine the likelihood of a spin flipping based on the spins of its neighboring points. This allows for the study of how the system's overall behavior changes as temperature and other variables are altered.

What are exact results on the Ising model?

Exact results on the Ising model refer to mathematical solutions that provide exact values for certain properties, such as the critical temperature or the magnetization, without the need for approximations. These results are often obtained through rigorous mathematical techniques, such as exact solutions on finite-sized lattices or through the use of advanced mathematical methods.

What is the significance of exact results on the Ising model?

Exact results on the Ising model allow for a deeper understanding of the system's behavior, as they provide precise values for key properties. They also serve as a benchmark for other theoretical and computational methods, allowing for the validation of approximate solutions. Furthermore, exact results can lead to the development of new theories and models.

What are some current research topics related to exact results on the Ising model?

Current research on exact results on the Ising model includes the study of higher-dimensional lattices, the effect of disorder on the system, and the behavior of the model in non-equilibrium conditions. Additionally, there is ongoing research on the application of exact results to other fields, such as quantum computing and machine learning.

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