Abstract
We prove a finite volume lower bound of the order $\sqrt{\log N}$ on the delocalization of a disordered continuous spin model (resp. effective interface model) in $d=2$ in a box of size $N$. The interaction is assumed to be massless, possibly anharmonic and dominated from above by a Gaussian. Disorder is entering via a linear source term. For this model delocalization with the same rate is proved to take place already without disorder. We provide a bound that is uniform in the configuration of the disorder, and so our proof shows that disorder will only enhance fluctuations.
Highlights
Our model is given in terms of the formal infinite-volume HamiltonianH[η] (φ) = 2 p(i − j)V − ηiφi (1)i,j i where the pair potential V (t) is assumed to be twice continuously differentiable with an upper bound V (t) ≤ c and V (t) = V (−t), i.e symmetric
We prove a finite volume lower bound of the order log N on the delocalization of a disordered continuous spin model in d = 2 in a box of size N
Our result will be valid for all choices of the potential V (t) and the random field configurations η for which the integrals in finite volume are well-defined
Summary
A simple fluctuation lower bound for a disordered massless random continuous spin model in D=2 Kulske, Christof; Orlandi, E. Document Version Publisher's PDF, known as Version of record. A simple fluctuation lower bound for a disordered massless random continuous spin model in D=2. More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverneamendment. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. For technical reasons the number of authors shown on this cover page is limited to 10 maximum
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