Critical system in condensed matter physics

[mimpim]

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.

 

[radium]

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.

 

[mimpim]

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.

 

[radium]

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.

 

[mimpim]

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?