Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Affiliates 
 Alumni 
 Visitors 
 Students 
 Research 
 ICAM-LANL 
 Publications 
 Publications 
 2007 
 2006 
 2005 
 2004 
 2003 
 2002 
 2001 
 2000 
 <1999 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Colloquia 
 Colloquia Archive 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 Archive 
 Kac Lectures 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Colloquia 
 
 Jobs 
 Students 
 Summer Research 
 Student Application 
 Visitors 
 Description 
 Past Visitors 
 Services 
 General 
 PD Travel Request 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Wednesday, November 01, 2017
10:00 AM - 11:00 AM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

CANCELLED

David Saad
Aston University

While macroscopic properties of hard-computational problems have been thoroughly investigated their manifestation in the corresponding microscopic configurations is much less understood. We introduce the notion of self-sustained clusters in Ising models, defined by the property that for each in-cluster spin, in-cluster field contribution dominates over the field induced by out-cluster spins; giving rise to highly stable configurations with respect to fluctuations. Self-sustained clusters shed light on the microscopic manifestation of metastable states and the emergence of frozen variables in constraint satisfaction problems. We discuss results obtained for the fully connected Ising and Sherrington-Kirkpatick (SK) models and present new results obtained for the p-spin model with p=3, which corresponds to the densely connected 3-XORSAT problem in the zero temperature limit; where the energy landscape undergoes an ergodicity breaking transition at a higher temperature than the spin-glass transition point. The analysis employs the (double) replica method to compute the entropy of macroscopic self-sustained clusters as a function of the temperature, their sizes and the difference between in-cluster and out-cluster induced fields. We observe that the self-sustained clusters are statically absent in the paramagnetic phase, but emerge at low temperatures when the computational problem becomes hard.

Host: Andrey Lokhov