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The Thermodynamic Limit in Mean Field Spin Glass Models
Abstract: We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as…
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Smoothing Effect of Quenched Disorder on Polymer Depinning Transitions
TLDR
It is proved that, as soon as disorder is present, the transition is at least of second order, in the sense that the free energy is differentiable at the critical line, so that the order parameter vanishes continuously at the transition.
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Fractional Moment Bounds and Disorder Relevance for Pinning Models
We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(·) of the location of the first contact of the (free) polymer with the defect line is assumed…
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A Replica-Coupling Approach to Disordered Pinning Models
We consider a renewal process τ =  {τ0, τ1,...} on the integers, where the law of τi − τi-1 has a power-like tail P(τi − τi-1 = n) = n−(α+1)L(n) with α ≥ 0 and L(·) slowly varying. We then assign a…
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Disorder relevance at marginality and critical point shift
Recemment, les predictions issues des methodes de groupe de renormalisation concernant l'influence du desordre pour les modeles d'accrochage ont ete rendus rigoureuses mathematiquement. La…
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About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean-field spin glass model
We consider the Sherrington-Kirkpatrick model and we prove that the quenched free energy per spin is strictly larger than the corresponding replica symmetric approximation, for all values of the…
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On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature
We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal…
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Marginal relevance of disorder for pinning models
TLDR
Here it is proved that disorder relevance is proved both for the general α = ½ pinning model and for the hierarchicalPinning model proposed by Derrida, Hakim, and Vannimenus, in the sense that a shift of the quenched critical point with respect to the annealed one is proved.
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Disordered pinning models and copolymers: Beyond annealed bounds
We consider a general model of a disordered copolymer with ad-sorption. This includes, as particular cases, a generalization of thecopolymer at a selective interface introduced by Garel et al.…
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Smoothing of depinning transitions for directed polymers with quenched disorder.
TLDR
It is proved that, as soon as disorder is present, the transition is at least of second order: the free energy is differentiable at the critical line, and the order parameter (contact fraction) vanishes continuously at the transition.
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