Critical point Definition and 56 Threads

I was reading a paper the other day that was discussing NFL behavior in heavy fermion systems. There was a phase diagram that was plotted as a function of temperature vs. doping. In the diagram, there was a transition from a spin glass state to an NFL phase which occurred as a second order T=0...

To distinguish a critical point is a saddle point or not, It is useful way to use discreminent. The discreminent is fxxfyy-fxy^2. What I want to know is how to prove the discreminent.

Ok so I am trying to do this problem and I have a question So based on the definition given in the book "An interior point of the domain of a function f where f' is zero or undefined is a critical point of f" This is the problem: y = sqrt(x^2 - 1) so y' = x/sqrt(x^2 - 1) to find a...

I have few questions about extrema of fonctions of two variables. It is written in my textbook: "At a local maximum, the gradient vector must be nul or undefined. A similar reasoning shows that the gradient must be nul at a local minimum." Actually there was no preceeding reasoning to this...

let f(x)=sin(1/x)*x^2 for x not 0, and f(0)=0. show that x=0 is a critical point for f which is neither a local minimum, a local maximum, nor an inflection point. well I tried differentiating this, and got f'=-cos(1/x) +2xsin(1/x). to find a critical point i make f'=0. Not sure how to do...

phase equilibrium -- beyond critical point In a phase diagram, at critical point, liquid phase is indistinguishable from vapour, and beyond which, only vapour can be found. Matter has four states, liquid, solid, gas and plasma. Can we include plasma state in a phase diagram? If yes, how should...