# Zero-Temperature Dynamics in the Dilute Curie–Weiss Model

@article{Gheissari2017ZeroTemperatureDI, title={Zero-Temperature Dynamics in the Dilute Curie–Weiss Model}, author={Reza Gheissari and Charles M. Newman and Daniel L. Stein}, journal={Journal of Statistical Physics}, year={2017}, volume={172}, pages={1009-1028} }

We consider the Ising model on a dense Erdős–Rényi random graph, $${\mathcal {G}}(N,p)$$G(N,p), with $$p>0$$p>0 fixed—equivalently, a disordered Curie–Weiss Ising model with $$\hbox {Ber}(p)$$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… Expand

#### 6 Citations

Local Minima in Disordered Mean-Field Ferromagnets

- Physics, Mathematics
- 2019

We consider the complexity of random ferromagnetic landscapes on the hypercube $$\{\pm \,1\}^N$$ { ± 1 } N given by Ising models on the complete graph with i.i.d. non-negative edge-weights. This… Expand

Nature Versus Nurture: Dynamical Evolution in Disordered Ising Ferromagnets

- Physics
- Statistical Mechanics of Classical and Disordered Systems
- 2019

We study the predictability of zero-temperature Glauber dynamics in various models of disordered ferromagnets. This is analyzed using two independent dynamical realizations with the same random… Expand

Nature vs. Nurture in Discrete Spin Dynamics

- Physics
- Sojourns in Probability Theory and Statistical Physics - I
- 2019

The problem of predictability, or “nature vs. nurture”, in both ordered and disordered Ising systems following a deep quench from infinite to zero temperature is reviewed. Two questions are… Expand

A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

- Physics
- 2016

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1… Expand

Friendly bisections of random graphs

- Mathematics
- 2021

Resolving a conjecture of Füredi from 1988, we prove that with high probability, the random graph G(n, 1/2) admits a friendly bisection of its vertex set, i.e., a partition of its vertex set into two… Expand

Stable and Metastable Phases for the Curie–Weiss–Potts Model in Vector-Valued Fields via Singularity Theory

- Physics, Mathematics
- 2020

We study the metastable minima of the Curie-Weiss Potts model with three states, as a function of the inverse temperature, and for arbitrary vector-valued external fields. Extending the classic work… Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Zero temperature dynamics of Ising model on a densely connected
small world network

- Physics
- 2005

Abstract.The zero temperature quenching dynamics of the ferromagnetic Ising model
on a densely connected small world network is studied where long range
bonds are added randomly with a finite… Expand

Zero-temperature dynamics for the ferromagnetic Ising model on random graphs

- Mathematics
- 2002

We consider Glauber dynamics at zero temperature for the ferromagnetic Ising model on the usual random graph model on N vertices, with on average γ edges incident to each vertex, in the limit as N→∞.… Expand

Disorder chaos and multiple valleys in spin glasses

- Mathematics, Physics
- 2009

We prove that the Sherrington-Kirkpatrick model of spin glasses is chaotic under small perturbations of the couplings at any temperature in the absence of an external field. The result is proved for… Expand

Zero-temperature dynamics of Ising spin systems following a deep quench: results and open problems

- Physics
- 2000

We consider zero-temperature, stochastic Ising models σt with nearest-neighbor interactions and an initial spin configuration σ0 chosen from a symmetric Bernoulli distribution (corresponding… Expand

Long-time predictability in disordered spin systems following a deep quench.

- Physics, Medicine
- Physical review. E
- 2017

It is conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. Expand

Extremal Cuts of Sparse Random Graphs

- Computer Science, Mathematics
- ArXiv
- 2015

The derivation relates the free energy of the anti-ferromagnetic Ising model on such graphs to that of the Sherrington–Kirkpatrick model, with P∗≈0.7632 standing for the ground stateEnergy of the latter, expressed analytically via Parisi's formula. Expand

Ising models on locally tree-like graphs

- Mathematics, Physics
- 2010

We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that… Expand

Analytic theory of the ground state properties of a spin glass. II. XY spin glass

- Physics
- 1980

For pt.I see ibid., vol.10, no.12, p.2769 (1980). The general theory, developed in the preceding paper to study the ground state properties of spin glasses, is applied to two-component spin systems.… Expand

Random Matrices and complexity of Spin Glasses

- Mathematics, Physics
- 2010

We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy… Expand

On multiple peaks and moderate deviations for supremum of Gaussian field

- Mathematics
- 2013

We prove two theorems concerning extreme values of general Gaussian fields. Our first theorem concerns with the concept of multiple peaks. A theorem of Chatterjee states that when a centered Gaussian… Expand