Topics in Statistical Physics
Phase transitions and critical phenomena
Thermodynamics of phase transitions (in part from PHY525)
- Phase diagram of a pure pVT
system
- Phase diagram of a
"normal" substance [tsl3]
- Phase diagram of H2O
[tsl4]
- Phase diagram of carbon [tsl6]
- Ferrimagnetic phases [tsl49]
- Liquid crystal phases [tsl51]
- Ordering of surfactant molecules [tsl50]
- Phase coexistence: Gibbs phase rule [tln27]
- Classification of phase transitions [tln28]
- Gibbs free energy and derivatives at discontinuous
transition [tsl7]
- Gibbs free energy and derivatives at continuous
transition [tsl8]
- Clausius-Clapeyron equation [tln29]
- Entropy of a supercooled liquid [tex30]
- Coexistence line of continuous phase
transition [tex37]
- Heat capacity of vapor in equilibrium
with liquid phase [tex41]
- Discontinuous transition: change in
internal energy [tex123]
- Latent heat and response functions [tex124]
- Dry ice [tex125]
- Abnormal phase behavior [tex54]
- Law of corresponding states [tln30]
- Guggenheim plot [tsl9]
- Van der Waals equation of state with coexistence curve
[tsl10]
- Maxwell
construction [tln31]
- Gibbs and Helmholtz free energies of the van der Waals
fluid
at T<Tc [tsl11]
- Condensation and evaporation [tln32]
- Dieterici equation of state [tex34]
- Melting or freezing [tex51]
- Triple point phase changes [tex52]
- Helium liquids [tln33]
- Phase diagram of 4He [tsl13]
- Phase diagram of 3He [tsl14]
- Exotic properties of helium II [tln34]
- Thermodynamics of a superconductor
- Superconducting transition [tln35]
- Thermodynamics of a ferromagnet [tsl5]
- Structural transitions of iron [tex53]
- Phase coexistence of ammonia [tex55]
- Latent heat and heat capacities at superconducting
transition [tex44]
Mean-field theory and Ginzburg-Landau theory
- Mean-field model of ferromagnet (from equations of state)
- Ginzburg-Landau theory of continuous transition
- Ginzburg-Landau theory of discontinuous transition
- Van der Waals gas as mean-field model
- Critical-point singularities
- Critical exponents of magnetic system
- Critical exponents of fluid system
- Mean-field values of critical exponents
- Exponent inequalities
Simple microscopic models systems
- Lattice versus continuum
- Role of dimensionality
- Ising model
- Potts model
- Vertex model
- XYZ model
- n-vector model
- Ordering and fluctuations
- Universality in critical behavior
Ising model
- Application to magnetism
- Application to metallic alloy
- Application to lattice gas
- T=0 phase diagrams of Ising spin chains
- Mean-field approximation
- Bragg-Williams approximation
- Bethe approximation
- Equivalent-neighbor coupling
Transfer matrix method
- Ising chains
- Further neighbor coupling
- Alternating coupling
- Correlation functions
- n-vector chains
- Ising model in two dimensions
- Ising lattice gas
Scaling theory
Renormalization group theory
Aspects of complexity
Looking beyond reductionist program:
- Cybernetics
- Synergetics
- Systems theory
- Science of complexity
Key features:
- Adaptivity
- Emergent attributes (functions)
- Self-organisation
- Network structures (hierarchy, hubs, scale-free, fractal)
- Self-replication
- Global decisions from local information
- Random explorations and focused processes (chance and
necessity)
- Edge of chaos
Methodology:
- Genetic algorithms [psl1] [psl3]
- Cellular automata [psl2]
Complexity in classical dynamics
Phase portraits of simple dynamical systems (in part from
PHY520)
Hamiltonian chaos (in part from PHY520)
- Integrability as a universal or contingent property [mln98] [mln99]
[msl15]
- Poincaré surface of section [mln100]
- Toda system (integrable) [msl12]
- Hénon-Heiles system (nonintegrable) [msl13]
Dissipative chaos (in part from PHY520)
- Dissipative dynamical systems [mln101]
- Fixed points in 3D phase flow [msl16]
- Limit cycles in 3D phase flow [msl17]
- Toroidal attractor in 3D phase flow [msl18]
- Strange attractor in 3D phase flow [msl19]
- Rössler band
- Lorenz attractor
Chaos in iterated maps
- Iterated maps
- Logistic model (continuous time) [mln32]
[mex107]
- Logistic map (discrete time) [mln34]
- Period-doubling route to chaos [msl35] [msl41]
- Universal features
Algorithmic complexity
Anharmonicities in vibrations (in part from PHY520)
- Linearly damped harmonic oscillator [mln6]
- Harmonic oscillator with attenuation [pmex12]
- Driven harmonic oscillator [mln28]
[mln29] [pmln1]
- Amplitude resonance [msl48]
- Lattice vibrations and normal modes [mln43]
[mln30] [mln48]
- Molecular vibrations [pmln2]
- Parametric resonance
- Anharmonic vibrations
- Effects of anharmonicity on resonance
Complexity in stochastic processes
Markov processes
Irreversibility, arrow of time, entropy, and information
Emergent qualities
Dissipative structures
Self-organization
Interactions -> structures -> functions
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Last updated 06/10/16