In statistical physics and solid state physics at zero temperature (T=0), there are various quantum phase transitions that can be 1st order phase transitions or continuous (2nd order) phase transitions. One way to distinguish the two is to look at [the free energy and to see the critical exponents](https://en.wikipedia.org/wiki/Phase_transition). ;
1. What are some examples of phase transitions in Supersymmetry (SUSY) gauge theories at zero temperature (T=0)? Are there both continuous (2nd order) phase transitions, and 1st order phase transitions?
2. What are some examples of phase transitions in Supersymmetry (SUSY) gauge theories at finite temperature (T>0)? Are there both continuous (2nd order) phase transitions, and 1st order phase transitions?
Note:
(i) Here let us consider phase transitions in a more physical ground, based on tuning the relevant operator deformations (additional terms in the Lagrangian, e.g. qLdeform) at the UV high energy, and see what it flows to at IR.
(ii) Other types of physical tuning parameters are chemical potential μ (zero T) and temperature T (to finite T), the μ-T are meaningful in the sense of QCD phase diagram.
(iii) If one had considered the physical relevant operator deformations (i) and (ii), then one can consider other non-physical tuning parameters, such as the number of color Nc, flavor Nf, etc. These types of parameters are much meaningless in the experiments.