Configuration Space
- Boundary condition (lattice spin system)
- Configuration space (lattice)
- External-field coupling
- Finite-range interaction (lattice)
- Interaction potential (Φ)
- Lattice Hamiltonian
- Spin configuration
- Spin space
- Translation-invariant interaction
Gibbs Measures
- DLR Gibbs measures satisfy a spatial Markov property
- DLR equation
- DLR existence theorem
- Extremal Gibbs measure
- Extremal Gibbs measures are ergodic (pure phases)
- Finite-volume Gibbs measure
- Gibbs specification
- Infinite-volume Gibbs measure
- Lattice partition function
- Lattice pressure (finite volume)
- Mixtures of Gibbs measures
- Pure phase
- Variational principle for lattice pressure
Phase Transitions
- 1D Ising model: no phase transition at positive temperature
- 2D Ising model: finite-temperature phase transition
- Order parameter
- Phase transition (Gibbsian viewpoint)
- Spontaneous magnetization
- Spontaneous symmetry breaking
- Spontaneous symmetry breaking and symmetry groups
- TFAE: Indicators of a Phase Transition