Spontaneous symmetry breaking - long range order 5 Ginzburg-Landau - - PowerPoint PPT Presentation

Critical exponents

singular behavior at T=Tc+/-

heat capacity susceptibility correlation length

disordered

• rdered

T

Tc

• rder parameter

disordered

• rdered

T

Tc control parameter

1

singular behavior at T=Tc+/-

control parameter

• rder parameter

correlation function scaling laws Rushbrooke scaling: Widom scaling: Fisher scaling: Josephson scaling:

H m

Critical exponents

2

Fisher scaling: general correlation function susceptibility

Critical exponents

3

Mean field exponents:

Critical exponents

4

Spontaneous symmetry breaking - long range order Ginzburg-Landau theory (Ising model of ferromagnet)

• rder parameter

high symmetry low symmetry

choice between 2 states time reversal

broken symmetry two-fold degeneracy

free energy functional

U scalar (invariant) under symmetry operations in

space group time reversal

5

correlation function

for

long range order

correlation over arbitrary distance

Spontaneous symmetry breaking - long range order 6