Lectures: 2:15-3:45 pm, Monday and Wednesday, HCB 207 (HCB Classroom Building).

Professor : Vladimir Dobrosavljevic, 611 Keen Building or A315 MagLab, 644-9755 or 644-5693, vlad@magnet.fsu.edu

Office Hours: by appointment. You are also welcome to contact me whenever you have questions.

Description:

The theory of phase transitions and critical phenomena is one of the most important chapters of modern many-body physics. Examples of phase transitions range from melting of ice and magnetization of ferromagnets to superfluidity and superconductivity. The behavior of many superficially different physical systems near a phase transition proves to be qualitatively the same, as it depends only on the symmetry of the problem and the spatial dimensionality. The last twenty five years have seen a rapid development of theoretical methods appropriate for these problems, which are based on scaling ideas and renormalization group method for classical and quantum many-body systems. These developments have by now become a standard language of modern Theoretical Physics, and as such should be regarded as an indispensable component in the training of graduate students not only in Condensed Matter, but also in Nuclear and High Energy Physics.

Objectives of this course:

This course will include a broad overview of the phenomena and systems displaying phase transitions,

It will provide an introduction to the basic theoretical methods used to describe them.

More advanced applications will be described more briefly, but appropriate literature will be given.

Prerequisite: Statistical Mechanics (PHY5524).

Topics covered in this course:

• Experimental systems showing classical and quantum critical phenomena.
• Thermodynamic potentials. Heat capacity. Magnetic susceptibility.
• Phases. Phenomenology of 1st order phase transitions. Continuous transitions.
• Landau theory. Order parameters. Spontaneous symmetry breaking.
• Critical behavior. Scaling. Critical exponents. Relations between critical exponents.
• Kadanoff scaling. Universality conjecture.
• Calculation of critical exponents: Real space RG methods.
• RG of Wilson and Fisher, Phi- 4 theory, 4- epsilon expansion.
• Continious symmetry: Mermin-Wagner theorem.
• Non-linear sigma-model; 2 + epsilon expansion.
• Scaling theory of localization. Quark confinement in QCD.
• Topological order. Kosterlitz-Thouless phase transition.
• Quantum critical phenomena. Hertz-Millis theory. Dissipative quantum tunneling.

Lecture notes (by V. Dobrosavljevic)

Useful texts:

        Principles of Condensed Matter Physics, by P. M. Chaikin, and T. C. Lubensky (Cambridge University Press, 2000).

        Thermodynamics, by Enrico Fermi (Dover, 1956).

        Lectures on Phase Transitions and the Renormalization Group, by Nigel Goldenfeld (Westview Press, 1992).

        Quantum Phase Transition, by Subir Sachdev (Cambridge University Press, Second Edition, 2011).

Useful Web pages and review articles:

Ben Simons'  Lecture Notes: http://www.tcm.phy.cam.ac.uk/~bds10/phase.html (University of Cambridge).

M. E. Fisher: Renormalization group theory: Its basis and formulation in statistical physics, Rev. Mod. Phys. 70, 653-681 (1998). 

M. E. Fisher: The renormalization group in the theory of critical behavior, Rev. Mod. Phys. 46, 597-616 (1974)

Course Work:  There will be weekly homework assignments (50% of course grade), one midterm exam(20% of course grade), and one take home final exam (30% of course grade).

Attendance. A responsive and active attendance to class is highly recommended. I will keep track of and use it in determining the final grade for those cases that fall on the borderline between to grade ranges. I will assign up to 10% of extra-credit for class participation.

Assistance. Students with disabilities needing academic accommodations should: 1) register with and provide documentation to the Student Disability Resource Center (SDRC); 2) bring a letter to me from SDRC indicating you need academic accommodations and what they are. This should be done within the first week of class. This and other class materials are available in alternative format upon request.

Honor Code. Students are expected to uphold the Academic Honor Code published in the Florida State University Bulletin and the Student Handbook. The first paragraph reads: The Academic Honor System of Florida State University is based on the premise that each student has the responsibility (1) to uphold the highest standards of academic integrity in the student's own work, (2) to refuse to tolerate violations of academic integrity in the University community, and (3) to foster a high sense of integrity and social responsibility on the part of the University community.