Zero-Temperature Dynamics in the Dilute Curie–Weiss Model
| Autor: | Reza Gheissari, Daniel Stein, Charles M. Newman |
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| Rok vydání: | 2018 |
| Předmět: |
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Physics Curie–Weiss law Probability (math.PR) 010102 general mathematics FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) 01 natural sciences Maxima and minima Combinatorics 010104 statistics & probability Minimum cut FOS: Mathematics Partition (number theory) Ising model 0101 mathematics Zero temperature Greedy algorithm Mathematics - Probability Mathematical Physics |
| Zdroj: | Journal of Statistical Physics. 172:1009-1028 |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-018-2087-9 |
| Popis: | We consider the Ising model on a dense Erd��s--R��nyi random graph, $\mathcal G(N,p)$, with $p>0$ fixed---equivalently, a disordered Curie--Weiss Ising model with $\mbox{Ber}(p)$ 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 $\mathcal G(N,p)$ 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. 19 pages |
| Databáze: | OpenAIRE |
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