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- W3010780997 abstract "This paper continues a study initiated in [34], on the localization transition of a lattice free field on $mathbb Z^d$ interacting with a quenched disordered substrate that acts on the interface when its height is close to zero. The substrate has the tendency to localize or repel the interface at different sites. A transition takes place when the average pinning potential $h$ goes past a threshold $h_c$: from a delocalized phase $h h_c$ where the field sticks to the substrate. Our goal is to investigate the effect of the presence of disorder on this phase transition. We focus on the two dimensional case $(d=2)$ for which we had obtained so far only limited results. We prove that the value of $h_c(beta)$ is the same as for the annealed model, for all values of $beta$ and that in a neighborhood of $h_c$. Moreover we prove that in contrast with the case $dge 3$ where the free energy has a quadratic behavior near the critical point, the phase transition is of infinite order $$lim_{uto 0+} frac{ log mathrm{F}(beta,h_c(beta)+u)}{(log u)}= infty.$$" @default.
- W3010780997 created "2020-03-23" @default.
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- W3010780997 date "2019-01-01" @default.
- W3010780997 modified "2023-09-25" @default.
- W3010780997 title "Pinning and disorder relevance for the lattice Gaussian Free Field II: The two dimensional case" @default.
- W3010780997 doi "https://doi.org/10.24033/asens.2411" @default.
- W3010780997 hasPublicationYear "2019" @default.
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