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

Critical exponents 1 control parameter singular behavior at T=T c+/- heat capacity disordered ordered susceptibility correlation length T c T disordered ordered order parameter T c T

Critical exponents 2 control parameter singular behavior at T=T c+/- m order parameter H correlation function scaling laws Rushbrooke scaling: Widom scaling: Fisher scaling: Josephson scaling :

Critical exponents 3 Fisher scaling: general correlation function susceptibility

Critical exponents 4 Mean field exponents:

Spontaneous symmetry breaking - long range order 5 Ginzburg-Landau theory (Ising model of ferromagnet) high symmetry U order parameter low symmetry choice between 2 states time reversal two-fold degeneracy broken symmetry free energy functional scalar (invariant) under symmetry operations in space group time reversal

Spontaneous symmetry breaking - long range order 6 correlation function for long range order correlation over arbitrary distance