46 research outputs found
Topological aspects of geometrical signatures of phase transitions
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.Comment: REVTEX file, 4 pages, 5 figure
Analytical results for coupled map lattices with long-range interactions
We obtain exact analytical results for lattices of maps with couplings that
decay with distance as . We analyze the effect of the coupling
range on the system dynamics through the Lyapunov spectrum. For lattices whose
elements are piecewise linear maps, we get an algebraic expression for the
Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the
Lyapunov spectrum for a completely synchronized state is analytically obtained.
The critical lines characterizing the synchronization transition are determined
from the expression for the largest transversal Lyapunov exponent. In
particular, it is shown that in the thermodynamical limit, such transition is
only possible for sufficiently long-range interactions, namely, for , where is the lattice dimension.Comment: 4 pages, 2 figures, corrections included. Phys. Rev. E 68, 045202(R)
(2003); correction in pres
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