 00425 Leonardo F. Guidi, Domingos H. U. Marchetti
 Renormalization Group Flow of the TwoDimensional Hierarchical Coulomb Gas
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Oct 31, 00

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Abstract. We consider a quasilinear parabolic differential equation associated with
the renormalization group transformation of the twodimensional
hierarchical Coulomb system in the limit as the size of the block $
L\downarrow 1$. We show that the initial value problem is well defined in a
suitable function space and the solution converges, as $t\rightarrow \infty$,
to one of the countably infinite equilibrium solutions. The $j$th
nontrivial equilibrium solution bifurcates from the trivial one at $\beta
_{j}=8\pi /j^{2}$, $j=1,2,\ldots $. These solutions are fully described and
we provide a complete analysis of their local and global stability for all
values of inverse temperature $\beta >0$. Gallavotti and Nicol\'{o}'s
conjecture on infinite sequence of ``phases transitions'' is also addressed.
Our results rule out an intermediate phase between the plasma and the
KosterlitzThouless phases, at least in the hierarchical model we consider.
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