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• W2025264803 abstract "We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature $T_c$, the disorder and thermally averaged correlation function $B(r)$ of the phase field $theta(x)$, $B(r) = bar{<[theta(x) - theta(x+ r) ]^2>}$ behaves, for $r gg a$, as $B(r) simeq A(tau) ln^2 (r/a)$ where $r = |r|$ and $a$ is a microscopic length scale. We derive the RG equations up to cubic order in $tau = (T_c-T)/T_c$ and predict the universal amplitude ${A}(tau) = 2tau^2-2tau^3 + {cal O}(tau^4)$. The universality of $A(tau)$ results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute ${A}(tau)$ numerically and obtain a remarkable agreement with our analytical prediction, up to $tau approx 0.5$." @default.
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• W2025264803 date "2012-10-10" @default.
• W2025264803 modified "2023-10-15" @default.
• W2025264803 title "Super-Rough Glassy Phase of the Random Field<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:math>Model in Two Dimensions" @default.
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• W2025264803 doi "https://doi.org/10.1103/physrevlett.109.157205" @default.
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