Ordered phase in the two-dimensional randomly coupled ferromagnet

Abstract

True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive when the absolute value of the random interaction is weaker than the ferromagnetic interaction. This result demonstrates that in this parameter domain the spin glass like ordering temperature is non-zero for these systems, in strong contrast to the 2d Edwards-Anderson spin glass.Comment: 7 pages; 9 figures; revtex; new version much extende

Lack of a thermodynamic finite-temperature spin-glass phase in the two-dimensional randomly coupled ferromagnet

“…Our results show that the model introduced in Ref. [43] and studied in detail in subsequent publications [44][45][46] does not exhibit a finite-temperature spin-glass transition in the thermodynamic limit for values of the parameter λ where it is expected to show such behavior. In agreement with the results of Ref.…”

“…7 in Ref. [46], we estimate that the breakup length for λ = 0.75 is approxi- Fig. 1(b) for λ = 0.75 with Tc = 0. mately ≈ 9.…”

“…[44], however for larger system sizes and and better statistics, we show that, indeed, the thermodynamic limit is a paramagnetic phase at finite temperature. This also means that deducing a finite-temperature behavior from zero-temperature simulations can be dangerous when the system sizes are not in the thermodynamic limit [46]. Given recent interest in inducing finite-temperature spin-glass transitions in quasi-planar topologies [26], we conjecture that adding any set of interactions that do not grow with the system size to a nearestneighbor lattice will likely not result in a finite-temperature spin-glass transition.…”

“…Note that we determine the estimated value of θ for λ = 0.75 by performing a linear fit to the data of Ref. [46] (quality of fit ∼ 0.58 [53]) and estimate θ(λ) ≈ 1.083(3) − 1.12(4)λ, valid in the window λ ∈ [0.5, 1.1]. Furthermore, by inspecting Fig.…”

“…Here we want to study the thermodynamic properties of a model proposed by Lemke and Campbell [43]-later analyzed in much detail in Refs. [44][45][46]-that might have the desired finite-temperature spin-glass transition and, most importantly, be of a mostly planar topology that can easily be constructed with current superconducting flux qubits. Our results show that, unfortunately, for large enough system sizes the model is in a paramagnetic phase at finite temperatures for a parameter range where it is predicted to be a spin glass.…”