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Acceleration from a clustering environment
by Roi Holtzman, Christian Maes
Submission summary
Authors (as registered SciPost users):  Roi Holtzman 
Submission information  

Preprint Link:  https://arxiv.org/abs/2405.19432v1 (pdf) 
Date submitted:  20240604 10:41 
Submitted by:  Holtzman, Roi 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study the effects of correlations in a random environment on a random walker. The dependence of its asymptotic speed on the correlations is a nonperturbative effect as it is not captured by a homogeneous version of the same environment. For a slowly cooling environment, the buildup of correlations modifies the walker's speed and, by so, realizes acceleration. We remark on the possible relevance in the discussion of cosmic acceleration as traditionally started from the Friedmann equations, which, from a statistical mechanical point of view, would amount to a meanfield approximation. Our environment is much simpler though, with transition rates sampled from the onedimensional Ising model and allowing exact results and detailed velocity characteristics.
Author indications on fulfilling journal expectations
 Provide a novel and synergetic link between different research areas.
 Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work
 Detail a groundbreaking theoretical/experimental/computational discovery
 Present a breakthrough on a previouslyidentified and longstanding research stumbling block
Current status:
Reports on this Submission
Strengths
1) The impact of correlations in the random environment of a random walker is studied on a simple model in which the environment is generated from an Ising model.
2) A parallel is made with the darkenergy problem: the current understanding of the expansion of the universe is based on a meanfield analysis and the authors raise the point that the study of correlations might play a role.
3) The manuscript is well written and pleasant to read.
Weaknesses
1) The analysis is limited to the 1D case, which is known to be the geometry in which disorder has the most significant effects.
2) Most results come from an application of a formula derived by Derrida (J. Stat. Phys. 1983) to the specific model introduced in the manuscript.
Report
In this manuscript, the authors study the asymptotic speed of a random walker in a random environment. They consider a simple 1D model in which the environment is generated from a realisation of the Ising model and thus presents correlations. They discuss the impact of these correlations on the speed of the walker by fixing the magnetisation but varying the correlation length. They discover a variety of nontrivial behaviours, and in particular show that a cooling of the environment (with the magnetisation still fixed) can yield an acceleration of the walker. A parallel is drawn with the darkenergy problem and the acceleration of the expansion of the universe.
The paper is interesting, clear and well written, although some points could still be clarified (see below). The model is simple but has the advantage to yield exact results that are thoroughly examined. From a purely technical point of view, the results are obtained from a known formula of Derrida (J. Stat. Phys. 1983) and standard calculations on the Ising model. The interest of the manuscript relies on the analysis of these exact formulas and their physical implication. I am not qualified to judge if the parallel with the acceleration of the universe is relevant, but from an outsider's point of view, it seems reasonable to question the importance of correlations in this context. Finally, this paper raises many questions that call for followup work.
Requested changes
1) When the model is introduced in Section III.A, it would be useful to introduce explicitly the inverse temperature $\beta$ below Eq. (III.1) as the one of the Ising model, which thus controls the correlation length (recalled on page 9). At the moment it is not so clear in Section III.A that $\beta$ is a parameter of the Ising model.
2) Related point: in Eqs. (III.2) and (III.3) why does $\beta$ appear in the jump rates of the random walker? I would naively think there should be two different temperatures: the one controlling the environment (Ising) and the one controlling the walker. Why are they chosen to be related (via the parameters $a$ and $\epsilon$)?
3) The implication of the results for a "cooling environment" is discussed several times. However, all the study is conducted for a random walker in a given environment, so that these discussions assume that the temperature is changed adiabatically. This should be written explicitly (at the moment it is only briefly mentioned in the introduction).
4) In the second paragraph of the introduction, it is mentioned that a rich phenomenology is observed in a "cooling environment". At this stage it is not clear why the authors only consider the case of cooling. The motivation is implicit in the next paragraph (the universe is cooling down), but the case of increasing temperature could also be interesting from a stat mech point of view. Could the authors comment on that?
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