1. Functional Renormalization

14. unified description of scalar models for all d and N

15. Scalar field theory

16. Flow equation for average potential

17. Simple one loop structure –nevertheless (almost) exact

18. Infrared cutoff

19. Scaling form of evolution equation
On r.h.s. :
neither the scale k
nor the wave function
renormalization Z
appear explicitly.
Scaling solution:
no dependence on t;
corresponds
to second order
phase transition.
Tetradis …

20. unified approach choose N choose d choose initial form of potential
run !
( quantitative results : systematic derivative expansion in second order in derivatives )

21. Flow of effective potential
Ising model
CO2
Critical exponents
Experiment :
T* = K
p* =73.8.bar
ρ* = g cm-2
S.Seide …

22. Critical exponents , d=3
ERGE world
ERGE world

23. critical exponents , BMW approximation
Blaizot, Benitez , … , Wschebor

24. critical exponents , BMW approximation

25. end