arXiv subjects

C. Amoruso

Publications and source records attributed to C. Amoruso.

3 recordsLinked to original sources

arXiv2006

Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses

We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with $κ\approx 2.1$. An argument is given that their fractal dimension $d_f$ is related to their interface energy exponent $θ$ by $d_f-1=3/[4(3+θ)]$, which is consistent with the commonly quoted values $d_f \approx 1.27$ and $θ\approx -0.28$.

cond-mat.dis-nn↗

arXiv2005

Determining Energy Barriers by Iterated Optimization: The Two-Dimensional Ising Spin Glass

Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems or proteins. Here we present an approach, which is based on subdividing the configuration space in a hierarchical manner, leading to upper and lower bounds for the energy barrier separating two configurations. The fundamental operation is to perform a constrained energy optimization, where the degree of constraintness increases with the level in the hierarchy. As application, we consider Ising spin glasses, where the energy barrier which needs to be surmounted in order to flip a compact region of spins of linear dimension $L$ are expected to scale as $L^ψ$. The exponent $ψ$ is very hard to estimate from experimental and simulation studies. By using the new approach, applying efficient combinatorial matching algorithms, we are able to give the first non-trivial numerical bounds $0.25 < ψ< 0.54$ for the two-dimensional Ising spin glass.

cond-mat.dis-nn↗

arXiv2004

Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c \sim 0.103$ compared to the concentration $p_n\sim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.

cond-mat.dis-nn↗