Critical system in condensed matter physics

In summary, the conversation discusses quantum phase transitions at zero temperature, specifically in the context of the transverse Ising model. It is defined as a phase transition at J=h and has implications at nonzero temperature in the quantum critical region. The conversation also mentions topological phases of matter, where there is no symmetry breaking at the transition but the two states are distinct. In one dimension, there is no phase transition for the hopping model in a lattice, but calculating correlation functions can reveal important physics.
  • #1
mimpim
5
0
My question is a little general, and that is how we say that a system is a critical system? for example the transverse Ising model is a critical system? I think the answer is yes, since as we change the transverse field we see that there is a phase transition between ferromagnet and paramagnet phases. Thanks for any comment.
 
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  • #2
I think you are talking about a system that undergoes a quantum phase transition at a quantum critical point.

A quantum phase transition is defined as a phase transition at zero temperature by tuning some parameter (in the quantum ising model this is the transverse field). However although a QPT is defined as happening at T=0, it still has implications at nonzero temperature in the quantum critical region. This also exists in antiferromagnet transitions. In the cuprate superconductors when you look at a plot of T v doping, the area in between above the quantum critical point is called a strange metal.

You can actually only have an ordered state for the quantum ising model at T=0.
Look at the second edition of quantum phase transitions.
 
  • #3
radium said:
I think you are talking about a system that undergoes a quantum phase transition at a quantum critical point.

A quantum phase transition is defined as a phase transition at zero temperature by tuning some parameter (in the quantum ising model this is the transverse field). However although a QPT is defined as happening at T=0, it still has implications at nonzero temperature in the quantum critical region. This also exists in antiferromagnet transitions. In the cuprate superconductors when you look at a plot of T v doping, the area in between above the quantum critical point is called a strange metal.

You can actually only have an ordered state for the quantum ising model at T=0.
Look at the second edition of quantum phase transitions.
Thanks for the reply. It gave me lots if useful information. By your answers, it raised some more question for me.
1) by this definition of a critical system that goes through a phase transition by changing a parameter, the transverse Ising model would be a critical system??

2) having an ordered phase is a must for having a phase transition?

Thanks again.
 
  • #4
1. I wouldn't call these things critical systems, they are systems that undergo quantum phase transition at quantum critical points. The transverse ising model undergoes a quantum phase transition at J=h (it is self dual).

2. No, in topological phases of matter there is no symmetry breaking at the transition but the two states are distinct, by their topology. You can have a transition between a trivial insulator and a Z2 topological insulator just by tuning the spin orbit interaction to get band inversion. You don't break any symmetry going from one to the other but you do go from a topologically trivial system to a nontrivial system, and these two states cannot be smoothly connected.
 
  • #5
radium said:
1. I wouldn't call these things critical systems, they are systems that undergo quantum phase transition at quantum critical points. The transverse ising model undergoes a quantum phase transition at J=h (it is self dual).

2. No, in topological phases of matter there is no symmetry breaking at the transition but the two states are distinct, by their topology. You can have a transition between a trivial insulator and a Z2 topological insulator just by tuning the spin orbit interaction to get band inversion. You don't break any symmetry going from one to the other but you do go from a topologically trivial system to a nontrivial system, and these two states cannot be smoothly connected.

Thanks again for the explanations. Although I do not know much about topological insulator, but your explanation for (2) was convincing to me. Now I have one more question:
In one dimension (1D) there is no phase transition (for example for the 1D hopping model in a lattice) and if you could calculate the correlation functions, you will get that much physics?
 

1. What is a critical system in condensed matter physics?

A critical system in condensed matter physics refers to a material or system that is at the brink of undergoing a phase transition. This means that the system is in a state of criticality, where small changes in external conditions can result in significant changes in its properties.

2. What are some examples of critical systems in condensed matter physics?

Common examples of critical systems in condensed matter physics include magnets at their Curie temperature, liquids at their boiling point, and alloys at their melting point. These systems exhibit critical phenomena such as phase transitions, critical opalescence, and power law behavior.

3. How are critical systems in condensed matter physics studied?

Critical systems in condensed matter physics are typically studied through statistical mechanics, which uses mathematical models to describe the behavior of large collections of particles. Experimental techniques such as neutron scattering, X-ray diffraction, and nuclear magnetic resonance spectroscopy are also used to investigate the properties of these systems.

4. What are the practical applications of studying critical systems in condensed matter physics?

Studying critical systems in condensed matter physics has many practical applications, including the development of new materials with desired properties, such as high-temperature superconductors. It also helps in understanding natural phenomena, such as the behavior of matter in extreme conditions, and in the design of more efficient technologies, such as computer chips and batteries.

5. What are some current research topics in critical systems in condensed matter physics?

Some current research topics in critical systems in condensed matter physics include the study of topological phases of matter, the behavior of quantum critical systems, and the properties of critical systems in low-dimensional and disordered systems. Other areas of interest include the study of critical systems in biological systems and in the field of quantum information science.

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