caa a22 4500 467891761 CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10955-006-9142-7 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9142-7 On the High Density Behavior of Hamming Codes with Fixed Minimum Distance [Elektronische Daten] [Giorgio Parisi, Francesco Zamponi] We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n→∞, d→∞, d/n = δ. The problem is relevant for coding theory, and the best available bounds state that the maximum density of the system falls in the interval 1 ≤ ρ V d ≤ exp (n κ(δ)), being κ(δ) > 0 and V d the volume of a sphere of radius d. We find a solution of the equations describing the liquid up to an exponentially large value of $${\widetilde \rho}$$ ρ = ρ V d , but we show that this solution gives a negative entropy for the liquid phase for $${\widetilde \rho}$$ ρ >rsimn. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. Springer Science + Business Media, Inc., 2006 Coding theory nationallicence HNC equations nationallicence liquid theory nationallicence virial expansion nationallicence Parisi Giorgio Dipartimento di Fisica, Università di Roma "La Sapienza,”, P.le A. Moro 2, 00185, Roma, Italy aut Zamponi Francesco Laboratoire de Physique Théorique de l'École Normale Supérieure, 24 Rue Lhomond, 75231, Paris Cedex 05, France aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1145-1167 0022-4715 123:6<1145 2006 123 10955 https://doi.org/10.1007/s10955-006-9142-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9142-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Parisi Giorgio Dipartimento di Fisica, Università di Roma "La Sapienza,”, P.le A. Moro 2, 00185, Roma, Italy aut NATIONALLICENCE 700 1- Zamponi Francesco Laboratoire de Physique Théorique de l'École Normale Supérieure, 24 Rue Lhomond, 75231, Paris Cedex 05, France aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1145-1167 0022-4715 123:6<1145 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer