INVESTIGADORES
RISAU GUSMAN Sebastian Luis
artículos
Título:
Topology and phase transitions: The case of the short range spherical model.
Autor/es:
RISAU GUSMAN, SEBASTIAN; RIBEIRO TEIXEIRA, ANA C.; STARIOLO, DANIEL A.
Revista:
JOURNAL OF STATISTICAL PHYSICS
Referencias:
Año: 2006 p. 1231 - 1253
ISSN:
0022-4715
Resumen:
We characterize the topology of
the phase space of the Berlin-Kac spherical model in the context of the
so called Topological Hypothesis, for spins lying in hypercubic
lattices of dimension d. For zero external field we are able to
characterize the topology exactly, up to homology. We find that, even
though there is a continuum of changes in the topology of the
corresponding manifolds, for d ≥ 3 there are abrupt
discontinuities in some topological functions that could be good
candidates to associate with the phase transitions that occur at the
thermodynamic level. We show however that these changes do not
coincide with the phase transitions and conversely, that no topological
discontinuity can be associated to the points where the phase
transitions take place. At variance with what happens in the Mean Field
version of this same model, we show that these abrupt topological
changes are accessible thermodynamically. We conclude that,
even in short range systems, the topological mechanism does not seem to
be responsible for the triggering of a phase transition. We also
analyze the case of spins connected to a macroscopic number of (but not
all) neighbors, and find that, similar to the results found for the
fully connected version, in this case the topological hypothesis seems
to hold: the phase transition coincides with an accumulation point of
the topological changes present in configuration space. The question of
the ensemble equivalence in the short range spherical model is also
considered.