TY - JOUR

T1 - Behavior of the Lattice Gaussian Free Field with Weak Repulsive Potentials

AU - Sakagawa, Hironobu

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

PY - 2021/1

Y1 - 2021/1

N2 - We consider the d(≥3) - dimensional lattice Gaussian free field on ΛN: = [- N, N] d∩ Zd in the presence of a self-potential of the form U(r) = - bI(| r| ≤ a) , a> 0 , b∈ R. When b> 0 , the potential attracts the field to the level around zero and is called square-well pinning. It is known that the field turns to be localized and massive for every a> 0 and b> 0. In this paper, we consider the situation that the parameter b< 0 and self-potentials are imposed on ΛαN,α∈(0,1). We prove that once we impose this weak repulsive potential from the level [- a, a] , most sites are located on the same side and the field is pushed to the same level when the original Gaussian field is conditioned to be positive everywhere, or negative everywhere with probability 12, respectively. This result can be applied to show the similar path behavior for the disordered pinning model in the delocalized regime.

AB - We consider the d(≥3) - dimensional lattice Gaussian free field on ΛN: = [- N, N] d∩ Zd in the presence of a self-potential of the form U(r) = - bI(| r| ≤ a) , a> 0 , b∈ R. When b> 0 , the potential attracts the field to the level around zero and is called square-well pinning. It is known that the field turns to be localized and massive for every a> 0 and b> 0. In this paper, we consider the situation that the parameter b< 0 and self-potentials are imposed on ΛαN,α∈(0,1). We prove that once we impose this weak repulsive potential from the level [- a, a] , most sites are located on the same side and the field is pushed to the same level when the original Gaussian field is conditioned to be positive everywhere, or negative everywhere with probability 12, respectively. This result can be applied to show the similar path behavior for the disordered pinning model in the delocalized regime.

KW - Capacity

KW - Entropic repulsion

KW - Lattice Gaussian free field

KW - Pinning

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U2 - 10.1007/s10955-020-02676-z

DO - 10.1007/s10955-020-02676-z

M3 - Article

AN - SCOPUS:85098870510

VL - 182

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

M1 - 8

ER -