Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models

@inproceedings{Carpentier2000GlassTO,
  title={Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models},
  author={D. Carpentier and Pierre Le Doussal},
  year={2000}
}
We study via RG, numerics, exact bounds and qualitative arguments the equilibrium Gibbs measure of a particle in a $d$-dimensional gaussian random potential with {\it translationally invariant logarithmic} spatial correlations. We show that for any $d \ge 1$ it exhibits a transition at $T=T_c>0$. The low temperature glass phase has a non trivial structure, being dominated by {\it a few} distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists… 
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