Topological aspects of geometrical signatures of phase transitions

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice [Formula Presented] models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart to a phase transition. © 1999 The American Physical Society.