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arXiv:cond-mat/0003071 · Physical review. B, Condensed matter

Logarithmic corrections to the ground-state energy of finite spin−12 antiferromagnetic chains due to ferromagnetic end bonds

Jizhong Lou, Jianhui Dai, Shaojin Qin, Zhao-Bin Su, Lu Yu

Published Oct 1, 2000• 12 citations
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Abstract

We analyze the logarithmic corrections due to ferromagnetic impurity ending bonds of open spin-1/2 antiferromagnetic chains, using the density matrix renormalization group technique. A universal finite-size scaling $\ensuremath{\sim}1/(L\mathrm{ln}L)$ for impurity contributions in the quasidegenerate ground-state energy is demonstrated for a zigzag spin-1/2 chain at the critical next-nearest-neighbor coupling and the standard Heisenberg spin-1/2 chain, in the long-chain limit. Using an exact solution for the latter case it is argued that one can extract the impurity contributions to the entropy and specific heat from the scaling analysis. It is also shown that a pure spin-3/2 open Heisenberg chain belongs to the same universality class.

DOI
10.1103/physrevb.62.8600

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We address the question of weak versus strong universality scenarios for the random-bond Ising model in two dimensions. A finite-size scaling theory is proposed, which explicitly incorporates lnL\mathrm{ln} LlnL corrections (L(L(L is the linear finite size of the system) to the temperature derivative of the correlation length. The predictions are tested by considering long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings, along which free energy, spin-spin correlation functions, and specific heats are calculated by transfer-matrix methods. The ratio $\ensuremath{\gamma}/\ensuremath{\nu}$ is calculated and has the same value as in the pure case; consequently conformal invariance predictions remain valid for this type of disorder. Semilogarithmic plots of correlation functions against distance yield average correlation lengths ${\ensuremath{\xi}}^{\mathrm{av}}$, whose size dependence agrees very well with the proposed theory. We also examine the size dependence of the specific heat, which clearly suggests a divergency in the thermodynamic limit. Thus our data consistently favor the Dotsenko-Shalaev picture of logarithmic corrections (enhancements) to pure system singularities, as opposed to the weak universality scenario.
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