1202.0967 (V. A. Malyshev)

Critical states of strongly interacting many-particle systems on a
circle    [PDF]

V. A. Malyshev

In multicomponent systems with strong local interaction one can encounter
some phenomena absent in the standard systems of statistical physics and other
multicomponent systems. Namely, a system with $N$ components in the bounded
volume of order 1 (macroscale) has the natural microscale of the order
$\frac{1}{N}$. Applying the macroscopic force (of order 1) on the system, and
thus on any of its components, one normally gets changes on the macroscale
itself and simultaneously small, of the order $\frac{1}{N}$, changes of the
microcomponents. In the systems, considered below, with the strong Coulomb
repulsion between the particles, however, one can observe the influence of such
force on the equilibrium state only on a scale, much smaller that the standard
microscale. Otherwise speaking, the information about the macroforce is not
available neither on the macrocale nor on the standard microscale, but only on
a finer scale. If this phenomenon does not depend on the continuity properties
of the applied force, then the mere existence of the equilibrium depends
essentially on the continuity properties of the external force.

View original: http://arxiv.org/abs/1202.0967