Update README.md

README.md

@@ -34,42 +34,33 @@ tokenizer = AutoTokenizer.from_pretrained("benhaotang/llama3.2-1B-physics-finetu
 device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
 model.to(device)
 # Example usage
-text = "What is renormalization group flow in physcis?\n"
+text = "Give me a short intodcution to renormalization group(RG) flow in physcis?\n"
 inputs = tokenizer(text, return_tensors="pt").to("cuda")
 outputs = model.generate(**inputs, max_length=2048)
 print(tokenizer.decode(outputs[0], skip_special_tokens=True))
 ```
 
-Expected output:
+Example output:
 
-> The renormalization group flow is a method used in physics to study the behavior of systems at very small distances and high energies. It is a way to analyze the evolution of physical parameters in a system over time, taking into account the interactions between them. In essence, the renormalization group flow is a way of describing how a system evolves as it is scaled up or down in energy.
+> I'll start by explaining the concept of renormalization group flow, then we can discuss the different types of renormalization group flow and their applications.
 >
-> The renormalization group flow is based on the idea that the behavior of a system at small distances (i.e., low energies) is closely related to its behavior at large distances (i.e., high energies). The renormalization group is a mathematical framework that describes how physical parameters change as the energy of a system increases.
->
-> In the context of quantum field theory, the renormalization group flow is used to study the behavior of particles and forces in the early universe. It is particularly useful for understanding the evolution of the universe from the Planck era to the present day.
->
-> The renormalization group flow is a powerful tool for physicists, allowing them to analyze complex systems and understand their behavior at the smallest scales. It has been applied to a wide range of systems, including gauge theories, quantum field theories, and cosmological models.
->
-> Some of the key features of the renormalization group flow include:
->
-> * The evolution of physical parameters over time, taking into account the interactions between them
-> * The use of renormalization group equations to describe the behavior of the system
-> * The ability to study the behavior of systems at very small distances and high energies
-> * The use of the renormalization group to understand the evolution of the universe from the Planck era to the present day.
-> 
-> Overall, the renormalization group flow is a powerful tool for physicists, allowing them to analyze complex systems and understand their behavior at the smallest scales.
+> ## Step 1: Introduction to Renormalization Group (RG) Flow
+> The Renormalization Group (RG) is a theoretical framework used in physics to study the behavior of physical systems at very small distances or high energies. It is a powerful tool for understanding the dynamics of systems that exhibit scale invariance, meaning that their properties remain the same under certain transformations of their parameters.
 > 
-> Here are some examples of systems that have been studied using the renormalization group flow:
+> ## Step 2: RG Flow in Physics
+> In physics, the RG flow is a mathematical transformation that describes how physical parameters, such as energy or length, evolve over time or space in a system. It is typically represented as a map between a set of initial parameters and a set of final parameters, where the map is defined by a set of equations that describe how the parameters change as the system evolves. The RG flow is often used to study the behavior of systems at the critical point, where the system's properties change dramatically as the parameters change.
 > 
-> * The early universe: The renormalization group flow has been used to study the evolution of the universe from the Planck era to the present day, taking into account the interactions between particles and forces.
-> * Gauge theories: The renormalization group flow has been used to study the behavior of gauge theories, including the strong, weak, and electromagnetic forces.
-> * Quantum field theories: The renormalization group flow has been used to study the behavior of quantum field theories, including the behavior of particles and forces at very small distances and high energies.
-> * Cosmological models: The renormalization group flow has been used to study the evolution of the universe, taking into account the interactions between particles and forces.
+> ## Step 3: Types of RG Flow
+> There are several types of RG flow, including:
 > 
-> Some of the key researchers who have contributed to the development of the renormalization group flow include:
+> * **Continuum RG Flow**: This is the most common type of RG flow, where the system is treated as a continuum, and the equations of motion are derived from a set of partial differential equations.
+> * **Discrete RG Flow**: This type of RG flow is used in systems with discrete variables, such as lattice gauge theory.
+> * **Asymptotic RG Flow**: This type of RG flow is used in systems with a power-law dependence of the parameters on the energy scale.
+> * **Non-Asymptotic RG Flow**: This type of RG flow is used in systems with a logarithmic dependence of the parameters on the energy scale.
 > 
-> * Edward Witten: Witten is a physicist who has made significant contributions to the development of the renormalization group flow, particularly in the context of gauge theories and quantum field theories.
-> * Gerard 't Hooft: 't Hooft is a physicist who has made significant contributions to the development of the renormalization group flow, particularly in the context of gauge theories and quantum field theories.
-> * John Schwarz: Schwarz is a physicist who has made significant contributions to the development of the renormalization group flow, particularly in the context of gauge theories and quantum field theories.
+> ## Step 4: Applications of RG Flow
+> The RG flow is a powerful tool for understanding the behavior of physical systems at very small distances or high energies. Some of the applications of RG flow include:
 > 
-> Overall, the renormalization group flow is a powerful tool for physicists, allowing them to analyze complex systems and understand their behavior at the smallest scales. It has been applied to a wide range of systems, including gauge theories, quantum field theories, and cosmological models.
+> * **Quantum Field Theory**: RG flow is used to study the behavior of quantum field theories, such as the Standard Model of particle physics.
+> * **Condensed Matter Physics**: RG flow is used to study the behavior of materials at the nanoscale, such as superconductors and superfluids.
+> * **High-Energy Physics**: RG flow is used to study the behavior of high-energy particles, such as quarks and leptons.