A phase transition occurs when a system moves from a disordered state to an ordered one or vice-versa. Common phase transitions include melting and freezing, buckling, and ferromagnetism. An effective field model of of a phase transition approximates the transition with a polynomial potential, e.g., U(x) = Ax4 + (To-T) Bx2 where T is the current temperature, To is the transition temperature, and A and B are constants. The variable x is called the order parameter, and it describes how much order there is in the ordered state at a particular temperature. Take a system with: A = 208 J/m B = 53 J/(m2.K) To = 128 K (a) What is the maximum number of critical points for this potential? (b) What are the critical points for T = 64 K? [Enter the critical points from least (or most negative) to largest (most positive). For any extra critical points choose -255 (with no units) and neutral equilibrium. 0 m Type: OStable OUnstable ONeutral -255 Type: OStable OUnstable ONeutral 1-255 Type: OStable OUnstable ONeutral -255 Type: OStable OUnstable ONeutral -255 Type: OStable OUnstable ONeutral (c) What are the critical points for T = 256 K? [Enter the critical points from least (or most negative) to largest (most positive). For any extra critical points choose -255 (with no units) and neutral equilibrium. 2.85 m * Type: Stable OUnstable ONeutral 10 m Type: OStable OUnstable ONeutral Type: OStable OUnstable ONeutral -255 Type: OStable OUnstable ONeutral -255 Type: OStable OUnstable ONeutral