arXiv:cond-mat/9810180·v1·Statistical Mechanics
Topological aspects of geometrical signatures of phase transitions
Roberto Franzosi (1,5)🇮🇹 · Lapo Casetti (2)🇮🇹 · Lionel Spinelli (3,5)🇫🇷 · Marco Pettini (4,5) ((1) Dipartimento di Fisica, Universita` di Firenze, Italy; (2) INFM, Dipartimento di Fisica, Politecnico di Torino, Italy; (3) CPT - C.N.R.S., Marseille, France; (4) Osservatorio Astrofisico di Arcetri, Firenze, Italy; (5) INFM, UdR di Firenze, Firenze, Italy)🇮🇹
Abstract
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 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 of a phase transition.
Comments: REVTEX file, 4 pages, 5 figures