Renormalisation group - Which critical points are usefull in a RG flow diagram?

In summary, the Renormalisation Group (RG) is a mathematical framework used to study the behavior of physical systems at different length scales. It is commonly used in statistical mechanics and quantum field theory to understand how a system changes as we zoom in or out on it. The RG flow diagram is a graphical representation of this behavior and is useful in identifying critical points, which are points in a phase transition where a system undergoes a sudden change in behavior. There are three main types of critical points: stable, unstable, and semi-stable. Researchers use the RG flow diagram to predict the behavior of a system near a phase transition and to identify new critical points.
  • #1
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In a RG flow diagram for a physical system where we have two fix points, which one is the most important one and describes the physical theory of the system?
Is it the unstable fix point or the "stable" one where some of the flow lines flows towards?
 
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  • #2
It depends on what physical question you want to ask.

Take QCD as an example. To describe high-energy scattering processes, we calculate near the UV fixed point. To describe the low-energy hadron spectrum, we calculate (via monte carlo simulations in lattice gauge theory) near the IR fixed point.
 

1. What is the Renormalisation Group (RG)?

The Renormalisation Group is a mathematical framework used to study the behavior of physical systems at different length scales. It is commonly used in statistical mechanics and quantum field theory to understand how a system changes as we zoom in or out on it.

2. How is the RG flow diagram useful in understanding critical points?

The RG flow diagram is a graphical representation of how a physical system changes as we change the length scale at which we are observing it. Critical points, which are points in a phase transition where a system undergoes a sudden change in behavior, can be identified on the RG flow diagram. This helps us understand the behavior of the system at different scales and how it approaches the critical point.

3. What are the different types of critical points in a RG flow diagram?

There are three main types of critical points in a RG flow diagram: stable, unstable, and semi-stable. Stable critical points correspond to fixed points, where the system's behavior remains the same at all length scales. Unstable critical points correspond to limit cycles, where the system's behavior oscillates between two different states. Semi-stable critical points correspond to limit sets, where the system's behavior is chaotic and unpredictable.

4. Can critical points be used to predict the behavior of a system near a phase transition?

Yes, critical points in a RG flow diagram can be used to predict the behavior of a system near a phase transition. By studying the behavior of the system at different length scales and identifying the critical point on the RG flow diagram, we can understand how the system will behave near the critical point and how it will transition between different phases.

5. How do researchers use the RG flow diagram in their studies?

The RG flow diagram is a powerful tool used by researchers to study the behavior of physical systems. It allows them to understand how a system changes at different length scales and how it approaches critical points. Researchers can also use the RG flow diagram to make predictions about the behavior of a system near a phase transition and to identify new critical points that may not have been previously discovered.

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