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Course Co-ordinated by :
IIT Guwahati
Course Available from :
22-November-2013
NPTEL
Physics
Advanced Statistical Mechanics (Web)
Critical exponents
Modules / Lectures
Statistical Mechanics: A brief overview
Specification of macrostates
Ensemble and Ensemble average
Thermodynamics in different ensembles
Particles and Statistics
Problems and Hints 1
References 1
Phase Transition and Critical Phenomena
First and second order transitions
Critical phenomena
Morphology, fluctuation and correlation
Correlation, fluctuation and response
Problems and Hints 2
References 2
Critical exponents and exponent inequalities
Critical exponents
Scaling inequalities
How to study critical phenomena
Problems and Hints 3
References 3
Models and Universality
Ising model and its ground state
Ising model and its applications
Other models and their ground states
Universality in different models
Problems and Hints 4
References 4
Mean field theory
Mean field theory for Fluids
Critical exponent of a fluid system
Mean field theory for magnetic systems
Mean field equation of state and its solution
Mean field critical exponents
Correlation length and correlation function
Bethe approximation
Bethe approximation for 2d Ising model
Landau theory of phase transition
Critical exponents from Landau theory
Problems and Hints 5
References 5
Tranfer matrix method
Transfer matrix and 1d Ising model
Determination of magnetization
Susceptibility, specific heat and correlation length
Spin-1 Ising model and Potts model
2d Ising model
Problems and Hints 6
References 6
Series expansion technique
High temperature expansion and 1d Ising model
High and low temperature expansions for 2d Ising model
Duality and critical temperature
Approximation techniques
Problems and Hints 7
References 7
Monte Carlo method
Ensemble average in Monte Carlo method
Ergodicity, Detailed balance and Metropolis algorithm
Monte Carlo Simulation of 2d Ising model
Measurements and errors
Problems and Hints 8
References 8
Scaling and renormalization
Homogeneous Function
Homogeneity of free energy and scaling
Renormalization Group
Renormalization operation
Free energy function and correlation length
Critical exponents, fixed point and universality
Application of RG to 1d Ising Model
Critical exponents of 1d Ising model
Problems and Hints 9
References 9
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