Group Analysis of Classical Lattice Systems

Name: Group Analysis of Classical Lattice Systems
Author: C. Gruber

Definitions and group structure.
The duality transformation.
Duality relation for the correlation functions.
Phase transitions with spontaneous symmetry breakdown. Ergodic decomposition.
Series and cluster expansion an application of universality hypothesis a “generalized” droplet-model.
The partial trace transformation. Equation for the correlation functions and representation of the symmetry group.
Invariant equilibrium states and duality transformation for infinite systems.
Asano contraction and group structure. Analyticity properties of the free energy.
Analyticity and uniqueness of the invariant equilibrium state.
Definitions and group structure for systems with constraints.
Expansions for the partition function.
Partial trace method and equilibrium equations.
Duality transformation restricted to finite bonds.
Asano contractions and unicity of state.
General framework of higher spin systems.
Physical implications of the group structure.
Spin 1 lattice systems.
Zeroes of the partition function.