# Critical system in condensed matter physics

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1. Oct 2, 2015

### 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.

2. Oct 4, 2015

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. Oct 4, 2015

### mimpim

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. Oct 4, 2015