Critical exponents for the Heisenberg AFM spin-1/2 chain

In summary, the conversation is about the critical exponent and universality class of the Heisenberg antiferromagnetic spin-1/2 model in 1D. The speaker is also looking for a good article on this topic and asks about the critical behavior when moving away from criticality by altering the coupling or adding an external field. They also mention the use of bosonization in solving these types of spin problems. The critical exponent ν and correlation length ξ(ε) are also discussed.
  • #1
bpirvu
5
0
Hi everybody!

I'm looking for the critical exponent ν (i.e. the one of the correlation length) of the Heisenberg (i.e. equal coupling in all directions) antiferromagnetic spin-1/2 model in 1D...
Furthermore, do you know to which universality class it belongs? Is it true that it's the Kosterlitz-Thouless class? Do you know a good (review-) article about this topic? I couldn't find anything useful neither in Sachdev's book nor in Takahashi's one, but maybe I didn't check carfully enough...

One more question: there are two possible ways to move away from criticality in the case of the Heisenberg model, namely altering one of the coulpling s.t. you end up with the XXZ-model, or adding an external homogenous field, say in Z-direction. Do they both yield the same critical behaviour?

Many thanks!
 
Physics news on Phys.org
  • #2
i remember the <S_z(x)S_z(0)>=x^(1/2)

For these 1d spin problems, such as xxz model and the Heisenberg model in magnetic field, the standard method is bosonization.

Hope these help!
 
  • #3
yuanyuan5220 said:
i remember the <S_z(x)S_z(0)>=x^(1/2)

For these 1d spin problems, such as xxz model and the Heisenberg model in magnetic field, the standard method is bosonization.

Hope these help!

hmmm... i guess you mean x^(-1/2) for the power law decay at criticality... this would imply for the critical exponent η from Γ(x)~x^-(d-2+η) that η=3/2...
however, what i need is the critical exponent ν of the exponential decay when the system is not critical i.e. Γ(x,ε)~x^-(d-2+η)*exp(-x/ξ(ε)) where ξ(ε)=|ε|^-ν is the correlation length...
 

1. What is a critical exponent?

A critical exponent is a quantity that describes the behavior of a physical system at its critical point, where it undergoes a phase transition.

2. What is the Heisenberg AFM spin-1/2 chain?

The Heisenberg AFM spin-1/2 chain is a model system used in condensed matter physics to study the behavior of magnetic materials. It consists of a chain of spin-1/2 particles with antiferromagnetic interactions between them.

3. How do critical exponents relate to the Heisenberg AFM spin-1/2 chain?

Critical exponents are used to describe the behavior of the Heisenberg AFM spin-1/2 chain at its critical point. They can reveal important information about the nature of the phase transition and the critical behavior of the system.

4. What are the main factors that influence critical exponents for the Heisenberg AFM spin-1/2 chain?

The main factors that influence critical exponents for the Heisenberg AFM spin-1/2 chain include the dimensionality of the system, the strength of the interactions between the spin particles, and the presence of any external fields or disorder.

5. Why are critical exponents important in studying the Heisenberg AFM spin-1/2 chain?

Critical exponents are important because they provide insight into the behavior of the Heisenberg AFM spin-1/2 chain at its critical point, which can be difficult to study experimentally. They also allow for comparisons between different physical systems and can help identify universal features of critical behavior.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
9
Views
5K
  • Beyond the Standard Models
Replies
24
Views
7K
  • Beyond the Standard Models
Replies
2
Views
2K
  • Science and Math Textbooks
Replies
19
Views
17K
Back
Top