Topology of configuration space of the mean-field phi4 model by Morse theory
Abstract
In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field φ4 model with a Z2 symmetry. Our purpose is discovering, if any, the relation between the second-order Z2-symmetry breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results at the light of two theorems on sufficiency conditions for symmetry breaking phase transitions recently proven. This study makes part of a research line based on the general framework of geometric-topological approach to Hamiltonian chaos and critical phenomena.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.