Advanced Statistical Physics Exam - 2nd Session

Set up the Taylor expansion of the Ginzburg-Landau free-energy function around x = 0 and find the critical line on which the coefficient of the quadratic term vanishes and the one

(Hint: as you shall use the probability of a linear combination of two Gaussian random variables in several steps of this and the following questions, first establish the form of

The co-planar spin configurations identified in the previous items are a sub-set of all ground states in this model.. The full manifold of ground states is disordered in the sense

One is interested in identifying the order parameter (in some cases this is easy, in others it is not), finding the critical curves of the control parameters in the phase

What do you conclude concerning the possibility of having an ordered state at low (but non-vanishing) temperatures and, therefore, a finite temperature phase transition from

We will now calculate the disorder averaged free-energy density of the model defined on the fully-connected graph with the replica method

Explain the Imry-Ma droplet argument that allows one to estimate in which dimension this model can sustain an ordered phase.... Draw an schematic

Take a random matrix with elements drawn from a Gaussian probability measure with zero average and variance σ 2.. Which is the probability density of the