Singular thermodynamic properties in random magnetic chains

作者：J. E. Hirsch, Jorge V. José · 发表于：Physical review. B, Condensed matter · 年份：1980 · DOI：10.1103/physrevb.22.5339 · 被引用次数：66 · 研究领域：Theoretical and Computational Physics、Physics of Superconductivity and Magnetism、Quantum many-body systems

The nearest-neighbor random-exchange Heisenberg antiferromagnetic Heisenberg chain ($s=\frac{1}{2}$) is studied at low temperatures via an approximate renormalization-group method. This entails renormalization of the random-exchange coupling constant $J$ and of the probability law for $J$. ${P}_{0}(J)$. After $n$ iterations we find that the renormalized probability function ${P}_{n}({J}^{(n)})$, a function of the renormalized coupling ${J}^{(n)}$, develops singular behavior for small ${J}^{(n)}$, independent of the initial form of ${P}_{0}(J)$. This happens both for ${P}_{0}(J)$ that diverge or go to zero as $J\ensuremath{\rightarrow}0$. The singular form of ${P}_{n}({J}^{(n)})$ is such that it leads to a specific heat and susceptibility that behave like $C\ensuremath{\sim}{T}^{1\ensuremath{-}{\ensuremath{\alpha}}_{C}(T)}$ and $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}{\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)}$. ${\ensuremath{\alpha}}_{C}(T)$ and ${\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)$ are exponents weakly dependent on temperature ($T$) that go to one as $T\ensuremath{\rightarrow}0$ and satisfy ${\ensuremath{\alpha}}_{\ensuremath{\chi}}(T)>{\ensuremath{\alpha}}_{C}(T)$, for arbitrary initial probability laws. The classical $n$-vector models, and in particular the classical Heisenberg model are also studied using a renormalization-group approach and it is found that their behavior is different than that of the quantum model: singular behavior in the therm...