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Critical system in condensed matter physics

  1. Oct 2, 2015 #1
    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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  3. Oct 4, 2015 #2


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    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.
  4. Oct 4, 2015 #3

    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.
  5. Oct 4, 2015 #4


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    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.
  6. Oct 4, 2015 #5
    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?
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