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Statistical Mechanics II: Statistical Physics of Fields >> Content Detail



Lecture Notes



Lecture Notes

SES #TOPICSLECTURE NOTES
L1

Collective Behavior, from Particles to Fields


Introduction, phonons and elasticity

(PDF)
L2

Collective Behavior, from Particles to Fields (cont.)


Phase transitions, critical behavior



The Landau-Ginzburg Approach


Introduction, saddle point approximation, and mean-field theory

(PDF)
L3

The Landau-Ginzburg Approach (cont.)


Spontaneous symmetry breaking and goldstone modes

(PDF)
L4

The Landau-Ginzburg Approach (cont.)


Scattering and fluctuations, correlation functions and susceptibilities, comparison to experiments

(PDF)
L5

The Landau-Ginzburg Approach (cont.)


Gaussian integrals, fluctuation corrections to the saddle point, the Ginzburg criterion

(PDF)
L6

The Scaling Hypothesis


The homogeneity assumption, divergence of the correlation length, critical correlation functions and self-similarity

(PDF)
L7

The Scaling Hypothesis (cont.)


The renormalization group (conceptual), the renormalization group (formal)

(PDF)
L8

The Scaling Hypothesis (cont.)


The Gaussian model (direct solution), the Gaussian model (renormalization group)

(PDF)
L9

Perturbative Renormalization Group


Expectation values in the Gaussian model, expectation values in perturbation theory, diagrammatic representation of perturbation theory, susceptibility

(PDF)
L10

Perturbative Renormalization Group (cont.)


Perturbative RG (first order)

(PDF)
L11

Perturbative Renormalization Group (cont.)


Perturbative RG (second order), the ε-expansion

(PDF)
L12

Perturbative Renormalization Group (cont.)


Irrelevance of other interactions, comments on the ε-expansion

(PDF)
L13

Position Space Renormalization Group


Lattice models, exact treatment in d=1

(PDF)
L14

Position Space Renormalization Group (cont.)


The Niemeijer-van Leeuwen cumulant approximation, the Migdal-Kadanoff bond moving approximation

(PDF)
L15

Series Expansions


Low-temperature expansions, high-temperature expansions, exact solution of the one dimensional Ising model

(PDF)
L16

Series Expansions (cont.)


Self-duality in the two dimensional Ising model, dual of the three dimensional Ising model

(PDF)
L17

Series Expansions (cont.)


Summing over phantom loops

(PDF)
L18

Series Expansions (cont.)


Exact free energy of the square lattice Ising model

(PDF)
L19

Series Expansions (cont.)


Critical behavior of the two dimensional Ising model

(PDF)
L20

Continuous Spins at Low Temperatures


The non-linear σ-model

(PDF)
L21

Continuous Spins at Low Temperatures (cont.)


Topological defects in the XY model

(PDF)
L22

Continuous Spins at Low Temperatures (cont.)


Renormalization group for the coulomb gas

(PDF)
L23

Continuous Spins at Low Temperatures (cont.)


Two dimensional solids, two dimensional melting

(PDF)
L24

Dissipative Dynamics


Brownian motion of a particle

(PDF)
L25

Continuous Spins at Low Temperatures (cont.)


Equilibrium dynamics of a field, dynamics of a conserved field

(PDF)
L26

Continuous Spins at Low Temperatures (cont.)


Generic scale invariance in equilibrium systems, non-equilibrium dynamics of open systems, dynamics of a growing surface

(PDF)

 








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