# Magnetisation and Mean Field Theory in the Ising Model

@article{Sakthivadivel2022MagnetisationAM, title={Magnetisation and Mean Field Theory in the Ising Model}, author={Dalton A R Sakthivadivel}, journal={SciPost Physics Lecture Notes}, year={2022} }

In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the…

## One Citation

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A simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms, providing a related, but alternative, formalism to those driven purely by descriptions of random dynamical systems, and taking a further step towards a comprehensive statement of the physics of self-organisation in formal mathematical language.

## References

SHOWING 1-10 OF 32 REFERENCES

### Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions

- Physics
- 1977

By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase…

### Critical behavior of the Ising model on the four-dimensional cubic lattice.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

It is found that within the given accuracy the canonical ensemble data are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical ensemble lends stronger support to a boundedspecific heat.

### A note on the Ising model in high dimensions

- Physics
- 1989

We consider thed-dimensional Ising model with a nearest neighbor ferromagnetic interactionJ(d)=1/4d. We show that asd→∞ the+phase (and the — phase) approaches a product measure with density given by…

### More is the Same; Phase Transitions and Mean Field Theories

- Physics
- 2009

This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related…

### Scaling and Renormalization in Statistical Physics

- Physics
- 1996

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory,…

### Correlations and Spontaneous Magnetization of the Two‐Dimensional Ising Model

- Mathematics
- 1963

In this paper we rederive, by simpler methods, the Onsager‐Kaufman formulas for the correlations and the Onsager formula for the spontaneous magnetization of the rectangular two‐dimensional Ising…

### The quantum theory of the electron

- Physics
- 1928

The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of…

### Statistical Mechanics:

- PhysicsNature
- 1937

AbstractPROF. R. H. FOWLER'S monumental work on statistical mechanics has, in this the second edition, in his own modest words, been rearranged and brought more up to date. But the new volume is much…