On the explicit construction of Parisi landscapes in finite dimensional Euclidean spaces
Abstract
An N-dimensional Gaussian landscape with multiscale translation-invariant logarithmic correlations has been constructed, and the statistical mechanics of a single particle in this environment has been investigated. In the limit of a high dimensional N → ∞, the free energy of the system in the thermodynamic limit coincides with the most general version of Derrida’s generalized random energy model. The low-temperature behavior depends essentially on the spectrum of length scales involved in the construction of the landscape. The construction is argued to be valid in any finite spatial dimensions N ≥1.
- Publication:
-
Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- December 2007
- DOI:
- 10.1134/S0021364007190137
- arXiv:
- arXiv:0706.3776
- Bibcode:
- 2007JETPL..86..487F
- Keywords:
-
- 64.60.Cn;
- 05.40.-a;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- 4 pages, no figures