Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Poster II
DY 29.39: Poster
Donnerstag, 28. Februar 2008, 16:00–18:00, Poster C
Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition — •Oliver Melchert and Alexander K. Hartmann — Institut für Physik, Universität Oldenburg, 26111 Oldenburg
We study domain walls in two-dimensional Ising spin systems in terms of a minimum-weight path problem. The disorder has a fraction ρ of ferromagnetic bonds and (1−ρ) of gaussian bonds with zero mean and unit width. We first study the magnetization to locate the critical point ρc, where the ferromagnet to spin-glass transition occurs. Further, for distinguished values of ρ close to the critical point, we investigate the stiffness exponent θ, which describes the scaling of the domain-wall energy with the system size L×L according to ΔE∼Lθ and we obtain the fractal dimension df, describing the scaling of the average domain-wall length, i.e. ⟨ ℓ ⟩∼Ldf. We perform a finite-size scaling analysis for systems up to L=512. We find that both exponents remain constant in the spin-glass phase, i.e. θ=−0.28(1) and df=1.274(1). This is consistent with conformal field theory, where it seems possible to relate the expontents via df−1 =3/[4(3+θ)]. Moreover we find that the scaling of the average domain-wall length near the critical point can be described by ⟨ ℓ ⟩∼Ldfcf[(ρ−ρc)L1/ν], with the critical fractal dimension dfc=1.221(1), the critical exponent of the correlation length ν=1.49(7) and a scaling function f[…].