Zero-Temperature Dynamics in the Dilute Curie–Weiss Model

Reza Gheissari, Charles Newman, Daniel L. Stein

Research output: Contribution to journalArticle

Abstract

We consider the Ising model on a dense Erdős–Rényi random graph, G(N, p) , with p> 0 fixed—equivalently, a disordered Curie–Weiss Ising model with Ber (p) couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of G(N, p) with p> 0 fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.

Original languageEnglish (US)
Pages (from-to)1009-1028
Number of pages20
JournalJournal of Statistical Physics
Volume172
Issue number4
DOIs
StatePublished - Aug 1 2018

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Ground State
Random Graphs
Local Minima
Ising model
Ising Model
ground state
Zero
Random Partitions
Absorbing
temperature
Disorder
partitions
disorders
Model
Configuration
configurations
Energy
Demonstrate
energy

Keywords

  • Constraint satisfaction
  • Curie–Weiss model
  • Dense random graph
  • Minimum cut
  • Random Ising model
  • Zero-temperature dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Zero-Temperature Dynamics in the Dilute Curie–Weiss Model. / Gheissari, Reza; Newman, Charles; Stein, Daniel L.

In: Journal of Statistical Physics, Vol. 172, No. 4, 01.08.2018, p. 1009-1028.

Research output: Contribution to journalArticle

Gheissari, Reza ; Newman, Charles ; Stein, Daniel L. / Zero-Temperature Dynamics in the Dilute Curie–Weiss Model. In: Journal of Statistical Physics. 2018 ; Vol. 172, No. 4. pp. 1009-1028.
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