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



Calendar / Schedule



Calendar

The calendar below provides information on the course's lecture (L), recitation (R), and exam (E) sessions.


SES #TOPICSKEY DATES
L1

Collective Behavior, from Particles to Fields


Introduction, phonons and elasticity

Problem set 1 out
L2

Collective Behavior, from Particles to Fields (cont.)


Phase transitions, critical behavior



The Landau-Ginzburg Approach


Introduction, saddle point approximation, and mean-field theory

L3

The Landau-Ginzburg Approach (cont.)


Spontaneous symmetry breaking and goldstone modes

L4

The Landau-Ginzburg Approach (cont.)


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

L5

The Landau-Ginzburg Approach (cont.)


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

Problem set 2 out
L6

The Scaling Hypothesis


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

Problem set 1 due
L7

The Scaling Hypothesis (cont.)


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

L8

The Scaling Hypothesis (cont.)


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

R1Recitation
L9

Perturbative Renormalization Group


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

Problem set 2 due
R2Recitation
E1In-class Test #1Problem set 3 out
L10

Perturbative Renormalization Group (cont.)


Perturbative RG (first order)

L11

Perturbative Renormalization Group (cont.)


Perturbative RG (second order), the ε-expansion

L12

Perturbative Renormalization Group (cont.)


Irrelevance of other interactions, comments on the ε-expansion

Problem set 4 out
L13

Position Space Renormalization Group


Lattice models, exact treatment in d=1

L14

Position Space Renormalization Group (cont.)


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

Problem set 3 due
R3Recitation
L15

Series Expansions


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

L16

Series Expansions (cont.)


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

Problem set 4 due
R4RecitationProblem set 5 out
E2In-class Test #2
L17

Series Expansions (cont.)


Summing over phantom loops

L18

Series Expansions (cont.)


Exact free energy of the square lattice Ising model

R5Recitation
L19

Series Expansions (cont.)


Critical behavior of the two dimensional Ising model

Problem set 5 due
L20

Continuous Spins at Low Temperatures


The non-linear σ-model

Problem set 6 out
L21

Continuous Spins at Low Temperatures (cont.)


Topological defects in the XY model

L22

Continuous Spins at Low Temperatures (cont.)


Renormalization group for the coulomb gas

L23

Continuous Spins at Low Temperatures (cont.)


Two dimensional solids, two dimensional melting

L24

Dissipative Dynamics


Brownian motion of a particle

R6Recitation
L25

Continuous Spins at Low Temperatures (cont.)


Equilibrium dynamics of a field, dynamics of a conserved field

Problem set 6 due
R6Recitation
E3In-class Test #3
L26

Continuous Spins at Low Temperatures (cont.)


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

Final project due 2 days after L26

 








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