Phase transistions and Partition functions

In summary, the conversation was about studying phase transitions in statistical mechanics and the curiosity about the partition function becoming zero. The Lee-Yang theorem was mentioned, but the whole program was not fully described. A request for a good paper on the subject was made, aside from Lee and Yang's work. Additionally, there was a question about the analytic properties of the partition function and whether it can be expanded and infinitely differentiated. It was mentioned that the Lee-Yang theorem specifically deals with the zeros of the partition function and a more detailed explanation can be found in the book Statistical Mechanics: Theory and Molecular Simulation. The partition function is generally not analytic, but rather can be represented as a Fourier transform. For more information on this, the book Advanced
  • #1
unchained1978
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I'm studying phase transitions in statistical mechanics, and I'm curious to know more about how the partition function becomes zero. I've read a bit about the Lee Yang theorem, but haven't found a good description of the whole program. Does anyone have a good paper on the subject? (Other than Lee and Yang's?)
Also, I can't figure out if the partition function itself is analytic in the sense that it can be expanded about some neighborhood and is infinitely differentiable. Can anyone shed some led on the analytic properties of partition functions?
Thanks
 
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  • #2
!The Lee-Yang theorem deals specifically with the zeros of the partition function. You can find a more detailed explanation in the book Statistical Mechanics: Theory and Molecular Simulation by Mark Tuckerman. As for the analytic properties of the partition function, it is generally not analytic, but rather can be represented as a Fourier transform of the probability distribution over the system's microstates. For more information, see the book Advanced Statistical Mechanics by Gregory Eyink.
 

FAQ: Phase transistions and Partition functions

What is the definition of a phase transition in physics?

A phase transition is a physical phenomenon that occurs when a system undergoes a sudden change in its properties, such as its state of matter, in response to a change in external conditions, such as temperature or pressure.

How do partition functions relate to phase transitions?

Partition functions are mathematical tools used to describe the statistical mechanics of a system. In the context of phase transitions, partition functions can be used to calculate the probability of a system existing in a particular phase, and how this probability changes as external conditions, such as temperature, are varied.

What is the difference between first and second order phase transitions?

In a first order phase transition, there is a discontinuity in the system's physical properties, such as energy or entropy, at the transition point. This results in a coexistence of two phases at the transition point. In contrast, a second order phase transition is characterized by a continuous change in physical properties at the transition point, with no coexistence of phases.

Can phase transitions occur in non-equilibrium systems?

Yes, phase transitions can occur in both equilibrium and non-equilibrium systems. However, the mechanisms and dynamics of the transitions may differ in these two types of systems.

How do external factors, such as pressure and magnetic field, affect phase transitions?

External factors, such as pressure and magnetic field, can affect phase transitions by altering the energy landscape of the system. This can change the stability and relative probabilities of different phases, resulting in a shift or change in the nature of the phase transition.

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