We reconsider the one-step replica-symmetry-breaking (IRSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of replica-symmetry breaking. Our approach extends the ideas of Montanari and Ricci-Tersenghi (2003 Eur. Phys. J. B 33 339) to more general combinatorial problems. It turns out that 1 RSB is always unstable at sufficiently small clause density a or high energy. In particular, the recent IRSB solution to 3-SAT is unstable at zero energy for alpha < alpha(m), with alpha(m) approximate to 4.153. On the other hand, the SAT-UNSAT phase transition seems to be correctly described within IRSB.
Instability of one-step replica-symmetry-broken phase in satisfiability problems / Andrea, Montanari; Parisi, Giorgio; RICCI TERSENGHI, Federico. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - STAMPA. - 37:6(2004), pp. 2073-2091. [10.1088/0305-4470/37/6/008]
Instability of one-step replica-symmetry-broken phase in satisfiability problems
PARISI, Giorgio;RICCI TERSENGHI, Federico
2004
Abstract
We reconsider the one-step replica-symmetry-breaking (IRSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of replica-symmetry breaking. Our approach extends the ideas of Montanari and Ricci-Tersenghi (2003 Eur. Phys. J. B 33 339) to more general combinatorial problems. It turns out that 1 RSB is always unstable at sufficiently small clause density a or high energy. In particular, the recent IRSB solution to 3-SAT is unstable at zero energy for alpha < alpha(m), with alpha(m) approximate to 4.153. On the other hand, the SAT-UNSAT phase transition seems to be correctly described within IRSB.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
