Critical exponents of quantum Heisenberg model

In summary, the quantum Heisenberg model is a theoretical model that describes the behavior of magnetic materials at the atomic level, taking into account quantum mechanical nature and spin interactions. Critical exponents are numerical values that describe the behavior of a system at its critical point, providing insights into its universal behavior. They are important in the quantum Heisenberg model as they allow us to understand and make predictions about magnetic materials. These exponents can be determined experimentally by studying the system at different temperatures and magnetic fields. While critical exponents can vary in different systems, they often fall into universality classes, allowing for generalizations and predictions about critical behavior.
  • #1
tomkeus
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Hey guys, I ran some simulation of thermal phase transition of three dimensional quantum antiferomagnetic cubic lattice. I'm pretty happy with critical temperature, but I'm not sure about critical exponents because I'm having trouble locating some reference with their best known values. I know that [tex]\gamma[/tex] should be something like 1.41 and I'm in the ballpark there, but I don't know anything about [tex]\alpha[/tex], [tex]\beta[/tex] and [tex] \nu[/tex].

Can anyone help me with this?
 
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  • #2
The critical exponents for a three-dimensional quantum antiferromagnetic cubic lattice are generally accepted to be \alpha = 0, \beta = 1/2, and \nu = 1/2. It is important to note that these values depend on the specific model of your simulation, so it's best to double check with the sources you used while constructing your model.
 

1. What is the quantum Heisenberg model?

The quantum Heisenberg model is a theoretical model in condensed matter physics that describes the behavior of magnetic materials at the atomic level. It takes into account the quantum mechanical nature of particles and their spin interactions.

2. What are critical exponents in the quantum Heisenberg model?

Critical exponents are numerical values that describe the behavior of a physical system at its critical point, where a phase transition occurs. In the quantum Heisenberg model, they represent the relationship between various physical properties, such as magnetization, temperature, and magnetic field, at the critical point.

3. Why are critical exponents important in the quantum Heisenberg model?

Critical exponents provide insights into the universal behavior of a system at its critical point, regardless of the specific details of the system. They allow us to understand the critical behavior of magnetic materials and make predictions about their properties at different temperatures and magnetic fields.

4. How are critical exponents determined experimentally?

Critical exponents can be determined experimentally by studying the behavior of a physical system at different temperatures and magnetic fields near its critical point. By plotting and analyzing the data, the critical exponents can be calculated and compared to theoretical predictions.

5. Can critical exponents change in different systems?

Yes, critical exponents can vary depending on the specific physical system being studied. However, they often fall into universality classes, where different systems exhibit similar critical behavior and have similar values for their critical exponents. This allows us to make generalizations and predictions about the critical behavior of a wide range of systems.

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