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- W1993377603 abstract "Diagrammatic valence-bond methods are introduced for $s=frac{1}{2}$ magnetic insulators whose random Heisenberg exchanges satisfy some distribution $f(x)$. Rapid solution of arbitrary 10-spin replicas yields, for the first time, complete static thermodynamics by generating successive replicas whose exchanges match $f(x)$. The usual singular distribution $J{x}^{ensuremath{-}ensuremath{gamma}}$ for structurally disordered tetracyanoquinodimethane (TCNQ) salts is contrasted with a nonsingular distribution for a random concentration $c$ of weak exchanges $ensuremath{epsilon}J$ along a chain of uniform $mathrm{Js}$. A renormalization procedure for interactions among odd segments at low temperature generates a wide range of couplings for a single $ensuremath{epsilon}>0$ and yields power laws for nonsingular $f(x)$. Experimental magnetic susceptibility $ensuremath{chi}(T)$, magnetization $M(T, H)$, and magnetic specific heat $C(T, H)$ results for the closely similar 1:2 complexes of quinolinium and acridinium with TCNQ are compared to $J{x}^{ensuremath{-}ensuremath{gamma}}$ and to interacting segments. The usual distribution has $ensuremath{gamma}=0.75$ and an enormous $J=2ifmmodetimeselsetexttimesfi{}{10}^{7}$ K, but fails to describe the $ensuremath{chi}(T)$ crossover around 20 K. Interacting segments fit $ensuremath{chi}(T)$ over the entire range, as well as available $M(T, H)$ and $C(T, H)$ data, for some $c=0.10$ weak exchanges $ensuremath{epsilon}J=70$ K among uniform exchanges $J=230$ K. Small differences between the two complexes were not parametrized. The microscopic picture of strong disorder leads to charge disproportionation on the TCNQ stack and to $J{x}^{ensuremath{-}ensuremath{gamma}}$, while weak disorder and supermolecular TCN$phantom{rule{0ex}{0ex}}{mathrm{Q}}_{2}^{ensuremath{-}}$ ion radicals rationalize the picture of weakly interacting segments." @default.
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- W1993377603 date "1980-08-15" @default.
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- W1993377603 title "Thermodynamics of random-exchange Heisenberg antiferromagnetic chains" @default.
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- W1993377603 doi "https://doi.org/10.1103/physrevb.22.1793" @default.
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