591 research outputs found
Importance of the topological defects for two dimensional phase transitions and their relevance for the renormalization group
For various two dimensional non linear models, we present a direct
comparison between the functions computed with the
renormalization group and the functions measured by Monte Carlo
simulations. The theoretical and measured functions match each other
nicely for models with a trivial topology, yet they disagree clearly for models
containing topological defects. In these later cases, they are compatible with
a phase transition at a finite temperature. This indicates that the global
properties of the manifold do matter, in contradiction with the assumption used
in the RG computation.Comment: RevTex file, 8 pages, to appears in Phys.Lett.
Heterogeneous volatility cascade in financial markets
Using high frequency data, we have studied empirically the change of
volatility, also called volatility derivative, for various time horizons. In
particular, the correlation between the volatility derivative and the
volatility realized in the next time period is a measure of the response
function of the market participants. This correlation shows explicitly the
heterogeneous structure of the market according to the characteristic time
horizons of the differents agents. It reveals a volatility cascade from long to
short time horizons, with a structure different from the one observed in
turbulence. Moreover, we have developed a new ARCH-type model which
incorporates the different groups of agents, with their characteristic memory.
This model reproduces well the empirical response function, and allows us to
quantify the importance of each group.Comment: 10 pages, 2 figures, To be published in Physica
- …