%0 Journal Article
%T Bimodal and Gaussian Ising spin glasses in dimension two
%+ Laboratoire Charles Coulomb (L2C)
%+ Physique Théorique (DPT)
%A Lundow, P. H.
%A Campbell, Ian
%< avec comité de lecture
%Z L2C:16-021
%@ 1539-3755
%J Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
%I American Physical Society
%V 93
%N 2
%P 022119
%8 2016-02-11
%D 2016
%R 10.1103/PhysRevE.93.022119
%Z Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]Journal articles
%X 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 criticalexponent $η ≡ 0$, 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 witha scaling variable $\tau_b = T^2/(1 + T^2)$ suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility $χ(\tau_b,L)$ and second moment correlation length $ξ (\tau_b,L)$ in the thermodynamic limit regime are extrapolated to the $\tau_b = 0$ 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.
%G English
%2 https://hal.science/hal-01289849/document
%2 https://hal.science/hal-01289849/file/PhysRe6.pdf
%L hal-01289849
%U https://hal.science/hal-01289849
%~ CNRS
%~ L2C
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021