Statistical physics for system of dipoles

In summary: Another possibility is to use a perturbation theory approach, where you start with the energies of a simpler system and then gradually add in the interactions between the polymers.In summary, the conversation discussed a project involving modeling the phase transition of 2 polymers with and without an external E-field. The approach being taken involves considering 2 types of dipoles and using a Monte Carlo simulation. Calculations have been made for the energies and partition functions for two different configurations of the dipoles, and the next step is to combine these energies in order to apply Flory theory. Possible approaches for combining the energies were also discussed, including using a weighted average or a perturbation theory approach.
  • #1
rolotomassi
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There is a project I'm working on to model the phase transition of 2 polymers with and without an external E-field. The approach I am taking is first to consider 2 types of dipoles, with a constant external field in the 'up' direction.

I'm thinking in two dimensions for now.

The dipoles can have 4 orientations and can be next to each other, or on top of one another giving 32 possible configurations. I know this is crying out for a Monte Carlo simulation which is an approach I am also pursuing however I'd like to progress analytically.

Having calculated the energies for the 2 cases, next to or on top of, I get 2 partition functions and 2 average energies.

I need to combine the two energies to get an overall average which I can work with in Flory theory. This is where I am having trouble.
 
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  • #2
How can I combine the two energies?One approach that may work is to use a weighted average of the two energies, where the weights are determined by the probabilities of the two configurations. In this case you would calculate the probability of each configuration based on its energy, then use those probabilities to calculate the weighted average of the energies.
 

What is statistical physics?

Statistical physics is a branch of physics that uses statistical methods and concepts to understand and predict the behavior of physical systems that consist of a large number of particles. It aims to explain macroscopic properties and behavior of matter from the microscopic interactions between individual particles.

What are dipoles in physics?

Dipoles are pairs of equal and opposite charges that are separated by a distance. They can be represented by arrows pointing from the negative charge to the positive charge, indicating the direction of the electric field. Dipoles are important in understanding the behavior of molecules and materials in electric fields.

What is the significance of statistical physics for systems of dipoles?

Statistical physics is important for understanding the collective behavior of systems of dipoles. It allows us to predict how dipoles will interact with each other and with external fields, and how this will affect the overall properties of the system. This is crucial for understanding the behavior of materials such as magnets and liquid crystals.

What are some common methods used in statistical physics for systems of dipoles?

Some common methods used in statistical physics for systems of dipoles include mean field theory, Monte Carlo simulations, and molecular dynamics simulations. These methods allow us to analyze the behavior of systems with a large number of particles and make predictions about their properties and behavior.

How does statistical physics for systems of dipoles relate to other branches of physics?

Statistical physics for systems of dipoles draws from concepts and methods in other branches of physics such as thermodynamics, quantum mechanics, and electromagnetism. It also has applications in other fields such as chemistry, materials science, and biology. Understanding the behavior of dipoles is essential for understanding many physical systems and phenomena.

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