Topology, Phase Transitions, and the Spherical Model

RISAU GUSMAN, SEBASTIAN; RIBEIRO TEIXEIRA, ANA C.; STARIOLO, DANIEL A.

PHYSICAL REVIEW LETTERS

American Physical Society

Año: 2005 vol. 95 p. 1457021 - 1457024

0031-9007

The topological hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the configuration space of the short range Berlin-Kac spherical model, for spins lying in hypercubic lattices of dimension $d$. We find a continuum of changes in the topology and also a finite number of discontinuities in some topological functions. We show, however, that these discontinuities do not coincide with the phase transitions which happen for $d geq 3$ and conversely, that no topological discontinuity can be associated with them. This is the first short range, confining potential for which the existence of special topological changes are shown not to be sufficient to infer the occurrence of a phase transition.