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.
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.
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.
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.
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.