2005/08/18 by Sebastián Risau-Gusman, S. Risau-Gusman, Ana C. Ribeiro-Teixeira +3 · 1 citation
Computer Science · Physics and Astronomy · #Scientific Research and Discoveries #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.95.145702
published as Phys. Rev. Lett. 95, 145702 (2005)
arxiv created 2005/08/18 · openalex publication_date 2005/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 > or = 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.