Entropic Repulsion of the Massless Field with a Class of Self-potentials

Sakagawa, Hironobu

doi:10.1007/s10955-009-9745-x

Cited by 3 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See review articles [17] and [29] for the background and development of these problems. [26] and [27] studied the effect of weak repulsive potentials instead of the hard wall. Also, disordered pinning of the form U x (r) = (βω(x) + h)I(|r| ≤ 1) has been studied in detail recently where β, h ∈ R and {ω(x)} x∈Z d is a family of i.i.d.…”

Section: Model and Resultsmentioning

confidence: 99%

“…Then, for the lower bound of the maximum, we can proceed the quenched-annealed comparison and the conditioning argument which have been developed in the study of the problem of entropic repulsion (cf. [3], [4], [26], etc.). The upper bound of the maximum is given by an FKG argument combining with the precise estimate on the number of large spikes for the m η N -field.…”

Section: On the Results And Strategy Of The Proofmentioning

confidence: 99%

See 1 more Smart Citation

On the Free Energy of a Gaussian Membrane Model with External Potentials

Sakagawa

2012

J Stat Phys

View full text Add to dashboard Cite

We consider a class of d-dimensional Gaussian lattice field which is known as a model of semi-flexible membrane. We study the free energy of the model with external potentials and show the following:(1) We consider the model with δ-pinning and prove that the field is always localized when d ≥ 4.(2) Consider the model confined between two hard walls. We give asymptotics of the free energy as the height of the wall goes to infinity.

show abstract

Section: Model and Resultsmentioning

confidence: 99%