Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment

TL;DR

This paper investigates how power-law decaying correlations in Gaussian environments influence the critical behavior of the random pinning model, revealing conditions under which disorder affects phase transitions.

Contribution

It provides new insights into the effect of correlated disorder on the critical properties of the pinning model, especially regarding the relevance of disorder based on correlation decay rates.

Findings

Annealed critical exponent matches pure case if a>2.

Disorder is relevant if correlations decay slowly enough (a>1).

Phase transition disappears when correlations are not summable (a<1).

Abstract

We study the random pinning model, in the case of a Gaussian environment presenting power-law decaying correlations, of exponent decay a>0. We comment on the annealed (i.e. averaged over disorder) model, which is far from being trivial, and we discuss the influence of disorder on the critical properties of the system. We show that the annealed critical exponent \nu^{ann} is the same as the homogeneous one \nu^{pur}, provided that correlations are decaying fast enough (a>2). If correlations are summable (a>1), we also show that the disordered phase transition is at least of order 2, showing disorder relevance if \nu^{pur}<2. If correlations are not summable (a<1), we show that the phase transition disappears.