Statistical and Thermal Physics 2E: Statistical Mechanics II

Chapter 7: The Chemical Potential and Phase Equilibria

Our focus is on a better understanding of the chemical potential and an introduction to phase transitions in many-particle systems and chemical reactions. Three programs explore the chemical potential in different ways.

Chapter 8: Classical Gases and Liquids

The ideal gas and the Debye theory of solids are among the very few systems in statistical mechanics that can be solved analytically. Approximation techniques are essential and usually require an analytically solvable reference system. For liquids there is no analytically solvable reference system, but the properties of a hard sphere fluid can be computed very accurately using computer simulations, making a system of hard spheres a useful reference system.

We use computer simulations to study the radial distribution function $g(r)$ which provides information on the spatial structure of a fluid. An important approximation technique for dense gases is the virial density expansion. We can use numerical integration to compute the integral needed to find the second virial coefficient $B_2$.

Chapter 9: Critical Phenomena

Landau theory is a mean-field theory approach to phase transitions. Although the theory does not usually provide accurate values for critical exponents, it provides a useful qualitative picture of phase transitions. The renormalization group method provides not just a calculation approach for determining the critical exponents, but also a conceptual understanding of phase transitions.

We will use the renormalization group to study the simplest statistical physics model, percolation as well as the Ising model.

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