2015/06/30 by P. H. Lundow, I. A. Campbell · 11 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Critical exponent #Degenerate energy levels #Exponent #Gaussian #Ground state #Ising model #Mathematical physics #Mathematics #Phase transition #Physics #Quantum mechanics #Scaling #Square lattice #Statistical physics #Theoretical and Computational Physics #Thermodynamic limit #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.93.022119
published in Physical review. E 93(2), 022119 (American Physical Society) · 10 pages, 18 figures
arxiv created 2015/08/27 · openalex publication_date 2016/02/11 · arxiv updated 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An analysis is given of numerical simulation data to size L=128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η≡0, and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T(*)(L) there is a regime of effectively continuous energy levels; below T(*)(L) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T(*)(L) tends to zero at very large L, leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t=T and with a scaling variable τ(b)=T(2)/(1+T(2)) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ(τ(b),L) and second moment correlation length ξ(τ(b),L) in the thermodynamic limit regime are extrapolated to the τ(b)=0 critical limit. The Gaussian critical exponent estimates from the simulations, η=0 and ν=3.55(5), are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η=0.20(2) and ν=4.8(3), distinctly different from the Gaussian critical exponents.