I’m currently studying the mean-field Ising model in the context of information theory, with a focus on its entropy, free energy, and connections to the Gibbs distribution. In particular, I’m working through the derivation of the partition function and the self-consistent equation of state:

$m^* = \tanh(\beta h + \beta J m^)$

where m^ is the magnetization, $\beta = 1/k_B T$ is the inverse temperature, h is the external magnetic field, and J is the coupling constant.

My primary interest lies in understanding this model as a probabilistic system, using tools like:

1. The entropy function to capture the uncertainty in spin configurations.
2. The minimization of the free energy to explain the emergence of collective behavior (magnetization).
3. The relationship between statistical mechanics and the large deviation principle for magnetization.

In my lectures, this problem is approached with a focus on information theory principles, emphasizing the interpretation of the Gibbs distribution as a probability measure over configurations.

I am looking for resources (books, papers, or lecture notes) that:

• Discuss the Ising model from a perspective similar to this (mean-field approximation and its relation to information theory).
• Provide detailed derivations of the partition function, the equation of state, and the role of entropy in the mean-field Ising model.

Any recommendations for comprehensive or specialized references would be greatly appreciated. Thank you!

I’m currently studying the mean-field Ising model in the context of information theory, with a focus on its entropy, free energy, and connections to the Gibbs distribution. In particular, I’m working through the derivation of the partition function and the self-consistent equation of state:

$m^* = \tanh(\beta h + \beta J m^)$

where m^ is the magnetization, $\beta = 1/k_B T$ is the inverse temperature, h is the external magnetic field, and J is the coupling constant.

My primary interest lies in understanding this model as a probabilistic system, using tools like:

1. The entropy function to capture the uncertainty in spin configurations.
2. The minimization of the free energy to explain the emergence of collective behavior (magnetization).
3. The relationship between statistical mechanics and the large deviation principle for magnetization.

In my lectures, this problem is approached with a focus on information theory principles, emphasizing the interpretation of the Gibbs distribution as a probability measure over configurations.

I am looking for resources (books, papers, or lecture notes) that:

• Discuss the Ising model from a perspective similar to this (mean-field approximation and its relation to information theory).
• Provide detailed derivations of the partition function, the equation of state, and the role of entropy in the mean-field Ising model.

Any recommendations for comprehensive or specialized references would be greatly appreciated.