$T \to 0$ mean-field population dynamics approach for the random 3-satisfiability problem
| dc.creator | Zhou, Haijun | |
| dc.date | 2007-12-31 | |
| dc.date | 2008-09-25 | |
| dc.date.accessioned | 2026-07-07T10:04:46Z | |
| dc.date.available | 2026-07-07T10:04:46Z | |
| dc.description | During the past decade, phase-transition phenomena in the random 3-satisfiability (3-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3-SAT problem by the mean-field first-step replica-symmetry-broken cavity theory at the limit of temperature $T\to 0$. The reweighting parameter $y$ of the cavity theory is allowed to approach infinity together with the inverse temperature $β$ with fixed ratio $r=y / β$. Focusing on the the system's space of satisfiable configurations, we carry out extensive population dynamics simulations using the technique of importance sampling and we obtain the entropy density $s(r)$ and complexity $Σ(r)$ of zero-energy clusters at different $r$ values. We demonstrate that the population dynamics may reach different fixed points with different types of initial conditions. By knowing the trends of $s(r)$ and $Σ(r)$ with $r$, we can judge whether a certain type of initial condition is appropriate at a given $r$ value. This work complements and confirms the results of several other very recent theoretical studies. | |
| dc.description | 10 pages with 5 figures. Extensively revised. PRE published version | |
| dc.identifier | https://arxiv.org/abs/0801.0205 | |
| dc.identifier | http://arxiv.org/abs/0801.0205 | |
| dc.identifier | PRE 77 (2008) 066102 | |
| dc.identifier | doi:10.1103/PhysRevE.77.066102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169801 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | $T \to 0$ mean-field population dynamics approach for the random 3-satisfiability problem | |
| dc.type | text |