# Course Contents

## Part A. Basic Statistical Mechanics

### Thermodynamics and phase transitions

#### Contents

Extensive and intensive quantities, equilibrium states and Gibbs spaces, stability conditions, the second law of thermodynamics, Legendre transforms. Phase transitions, order parameters, first and second order phase transitions. Scaling, homogeneous functions and critical indices.

#### References

*Thermodynamics*, article by M.J. Buckingham in*Phase Transitions and Critical Phenomena*, Vol 2, eds. C. Domb and M.S. Green, Academic Press, 1972.*Field Theory, the Renormalization Group and Critical Phenomena*, by D. Amit, World Scientific, Singapore, 1984.- B. Widom,
*Journal of Chemical Physics*43 (1965) 3898. *Universal Critical-Point Amplitude Relations*, article by V. Privman, P.C. Hohenberg and A.H. Aharony in*Phase Transitions and Critical Phenomena*, Vol 14, eds. C. Domb and J.L. Lebowitz, Academic Press, 1991.*Scaling, Universality and Operator Algebras*, article by L.P. Kadanoff, in*Phase Transitions and Critical Phenomena*, Vol 5A, eds. C. Domb and M.S. Green, Academic Press, 1975.

### Basic probability

#### Contents

State space and counting, combining probabilities, conditional probabilities and independence, Bayes' theorem. Probability distribution functions, moments and cumulants, charactersitic function, generating functions. Central limit theorem, sampling and errors.

#### References

*Probability and its Engineering Uses*by T.C. Fry, Van Nostrand, 1928.*Probability and Statistics*by M.H. DeGroot, Addison Wesley, 1986.*Introduction to Probability Models*by S.M. Ross, Academic Press, 1989.*Random Processes*by M. Rosenblatt, Oxford University Press, 1962.*Probability and Measure*by P. Billingsley, John Wiley and Sons, 1986.

### Classical and quantum ensembles

#### Contents

Stationary ensembles; the microcanonical and canonical ensembles; computer simulations and the Metropolis algorithm; grand canonical ensembles.

#### References

*Statistical Mechanics*by L. D. Landau and L. Lifschitz, Pergamon Press, 1977.*Statistical Mechanics*by R. K. Pathria, Pergamon Press, 1977.*Statistical Mechanics*by K. Huang, Wiley Eastern, 1988.*Pauli Lectures on Physics: Vol 4. Statistical Mechanics*by W. Pauli, ed. C.P. Enz, The MIT press, 1973.

### Ideal gases

#### Contents

Statistical approach to thermodynamics of ideal gases, the partition function; Bose condesation and phase transitions; electrons in a magnetic field: Landau levels and applications.

#### References

*Statistical Mechanics*by L. D. Landau and L. Lifschitz, Pergamon Press, 1977.*Statistical Mechanics*by R. K. Pathria, Pergamon Press, 1977.*Statistical Mechanics*by K. Huang, Wiley Eastern, 1988.*Pauli Lectures on Physics: Vol 4. Statistical Mechanics*by W. Pauli, ed. C.P. Enz, The MIT press, 1973.*Quantum Theory of Solids*by R. Peierls, Clarendon Press, 1955.

## Part B. Critical phenomena and phase transitions

### Introduction to lattice models

#### Contents

Random walks, scaling and critical exponents, continuum limit; percolation; spin models; gauge theories.

#### References

*Exactly solved models in statistical mechanics*by R. J. Baxter*Statistical field theory*by C. Itzykson and J.-M. Drouffe*Equilibrium statistical physics*by M. Plischke and B. Bergersen

### The Ising model

#### Contents

The Ising and Potts models, mean field theory, high and low temperature expansions, duality, Ginzburg-Landau theory, tricritical phenomena, the transfer matrix, Yang-Lee theory, real-space renormalisation.

#### References

*Exactly solved models in statistical mechanics*by R. J. Baxter*Statistical field theory*by C. Itzykson and J.-M. Drouffe*Equilibrium statistical physics*by M. Plischke and B. Bergersen

### O(N) models

#### Contents

O(N) models, Landau-Ginzburg theory, the renormalisation group, the Gaussian model and the Wilson-Fisher fixed point.

#### References

*Exactly solved models in statistical mechanics*by R. J. Baxter*Statistical field theory*by C. Itzykson and J.-M. Drouffe*Equilibrium statistical physics*by M. Plischke and B. Bergersen

© Sourendu Gupta. Created on Jun 11, 2001.