Introduction and Overview

Our first lecture was a guest lecture by Prof. Srinivas Raghu. He opened the class with a bright and cheerful introduction: ‘‘Um, welcome back, happy new year, et cetera.’’ Wonderful.

We covered a lot of material in this intro lecture, so I split it up into multiple pages. The first topic was about phase transitions.

Outline of Intro lecture

• Phase Transitions

  • Motivation of macroscopic properties, emergence

  • Drawing of phase diagram, explanation of P.T.s

  • Two types of phase transition: discontinuous first-order, or continuous higher-order

• Symmetry

  • Concept: high temperature phase, high symmetry; low temperature phase, broken symmetry

  • Example of gas vs solid

  • Example of tetragonal vs orthorhombic

• The Ising Model – in pgoress!

  • Motivation

  • Definition of problem, Hamiltonian

  • High temperature and Low temperature limits

  • Ground state breaks the symmetry

  • Phase diagram of the Ising Model

  • Peierl's intuitive argument for why there's a phase transition for d > 2

  • Dimensionality matters! No P.T. in 1D.

• Correlations – in progress!

  • another quantitative way to get at what's going on.

  • Correlation length is a fundamental divide between ‘‘microscopic’’ and ‘‘macroscopic’’

  • The corr. length diverges as you approach the critical point!

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