Zeros of the partition function (Yang-Lee and Fisher zeros)

In summary, the conversation discusses finding a resource for examining critical point behavior with derivations. The person mentions possibly reading about it in Jon Cardy's book, but is unable to find it again. Another person suggests Kardar's books, which go into detail about high and low temperature expansions of the 2-D Ising model, which is in line with what the first person is looking for. The first person agrees to check it out for helpful information.
  • #1
diegzumillo
173
18
Hey there,

Just wondering where I can get a nice treatment of this with derivations. I could swear I read about this in Jon Cardy's Scaling and renormalization in statistical physics but I can't find it again so maybe I was wrong.
 
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  • #2
Both of Kardar's books deal with examining critical point behavior. The second book goes into more detail with high and low temperature expansions of the 2-D Ising model. Is this along the lines of what you are looking for?
 
  • #3
NFuller said:
Is this along the lines of what you are looking for?
It certainly is. I'll give it a look to see if it has useful details for me.
 

Related to Zeros of the partition function (Yang-Lee and Fisher zeros)

1. What is the partition function in statistical mechanics?

The partition function is a mathematical concept used in statistical mechanics to describe the probability distribution of a physical system. It is a sum over all possible configurations of the system and is used to calculate various thermodynamic properties such as energy, entropy, and free energy.

2. What are Yang-Lee and Fisher zeros?

Yang-Lee and Fisher zeros are complex values of the parameters of the partition function where the system undergoes a phase transition. They are important in understanding the critical behavior of physical systems and can be used to determine the critical exponents of the system.

3. Why are the zeros of the partition function important?

The zeros of the partition function provide valuable information about the phase transitions and critical behavior of physical systems. They can help determine the critical temperature and order of the phase transition, as well as the universality class of the system.

4. How are the zeros of the partition function calculated?

The zeros of the partition function are typically calculated using numerical methods, such as Monte Carlo simulations, or analytical techniques, such as the Lee-Yang circle theorem. These methods involve solving for the roots of the partition function in the complex plane.

5. What are some applications of studying the zeros of the partition function?

Studying the zeros of the partition function has applications in various fields, such as condensed matter physics, quantum field theory, and computer science. It can help understand the behavior of physical systems near critical points and can also be used in the design of efficient algorithms for solving optimization problems.

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