Idealised models

Lattice models

• Barker-Fock model
• Blume-Emery-Griffiths model (including the Blume-Capel model)
• Bond fluctuation model
• Hard hexagon lattice model
• Hard square lattice model
• Henriques and Barbosa model
• Kagomé-lattice eight-vertex model
• Lattice gas
• Lattice hard spheres
• Lebwohl-Lasher model
• Potts model
  • Ashkin-Teller model
  • Kac model
• Roberts and Debenedetti model
• RP(n-1) model
• N-vector model:
  • Self-avoiding walk model (n=0)
  • Ising Models (n=1)
  • XY model (n=2)
  • Heisenberg model (n=3)
• Toda lattice
• Triangular lattice ramp model

Recommended reading

• Rodney J. Baxter "Exactly Solved Models in Statistical Mechanics", Academic Press (1982) ISBN 0120831821 (freely available pdf of book)

'Hard' models

• Hard core Yukawa
• Hard ellipsoid model
  • Hard ellipse model
• 1-dimensional hard rods
• 3-dimensional hard rods
• Hard pentagon model
• Hard sphere
  • Hard disks (in a two dimensional space)
  • Hard disks in a three dimensional space (including hard-cut spheres)
  • Hard hyperspheres
  • Dipolar hard spheres
• Hard spherocylinders
  • Charged hard spherocylinders
• Parallel hard cubes
• Sutherland potential
• Widom-Rowlinson model

Multi-site models

• Hard dumbbell model
• Branched hard sphere chains
• Flexible hard sphere chains (also known as the pearl-necklace model)
• Fused hard sphere chains
• Tangent linear hard sphere chains

Piecewise continuous models

• Buldyrev and Stanley model
• Hemmer and Stell model
• Hertzian sphere model
• Penetrable sphere model
• Penetrable square well model
• Ramp model (also known as the Jagla model)
• Square well model
• Square well lines potential
• Square well spherocylinders
• Soft-core square well model
• Square shoulder model
• Square shoulder + square well model
  • Double square well model
• Triangular well model

'Soft' models

• Born-Huggins-Meyer potential
• Buckingham potential
• Continuous shouldered well model
• Durian foam bubble model
• Flexible molecules (intramolecular interactions)
• Fomin potential
• Gaussian overlap model (including the Gaussian core model)
• Gay-Berne model
• Intermolecular Interactions
• Kihara potential
• Lennard-Jones model:
  • Lennard-Jones model in 1-dimension (rods)
  • Lennard-Jones model in 2-dimensions (disks)
  • Lennard-Jones model in 3-dimensions ('standard' model)
  • Lennard-Jones model in 4-dimensions
  • Lennard-Jones sticks
  • n-6 Lennard-Jones potential
  • 8-6 Lennard-Jones potential
  • 9-3 Lennard-Jones potential
  • 10-4-3 Lennard-Jones potential
  • Stockmayer potential
  • Two center Lennard-Jones model
• Mie potential
• Morse potential
• Patchy particles
• United-atom model
• Single site anisotropic soft-core potential
• Soft sphere potential

Charged or polar models

• Charged hard dumbbells
• Charged hard spherocylinders
• Dipolar hard spheres
• Keesom potential
• Quadrupolar hard spheres
• Restricted primitive model
• Shell model
• Stockmayer potential

Three-body potentials

• Many-body interactions - a general discussion page.
• Axilrod-Teller interaction

Metals

• Embedded atom model
• Finnis-Sinclair
• Gupta potential
• Sutton-Chen