8.4. -functions Consider a statistical system with the space of the coupling constants described by the variables

8.4. β-functions Consider a statistical system with the space of the coupling constants described by the variables (x,y2). The fixed point is identified by the origin (0,0). Suppose that the β

functions of these coupling constants are given by dx db

= −y2, dy2 db

= −2xy2.

Study the RG flows, with initial conditions (x0,y20

), and show that they are hyperboles in the plane (x,y). Identify the nature of the coupling constants, i.e. if they are relevant, irrelevant or marginal.