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Physical review. B, Condensed matter

Weak random bonds in the Heisenberg ferromagnet near two dimensions

Peter Kopietz

Published Sep 1, 1989• 5 citations
Publisher

Abstract

The quantum renormalization-group technique recently developed by Chakravarty and the present author is used to study weak random couplings in quantum-mechanical and classical nearest-neighbor Heisenberg ferromagnets in D=2+\ensuremath{\epsilon} dimensions and at low temperatures T. Momentum-shell recursion relations are obtained by considering the renormalization-group transformations of the cumulants of the probability distribution of the random exchange couplings. From a one-loop calculation it is found that, if the second cumulants ${\ensuremath{\sigma}}^{2}$ of the random couplings are smaller than a critical value ${\ensuremath{\sigma}}_{c}^{2}$, the only modification due to randomness in the low-temperature behavior of the order-parameter correlation length \ensuremath{\xi} in two dimensions is a renormalization of the spin stiffness ${\ensuremath{\rho}}_{s}$ according to ${\ensuremath{\rho}}_{s}$(X)=(1-X${)}^{\ensuremath{\varphi}}$${\ensuremath{\rho}}_{s}$(0), where X=${\ensuremath{\sigma}}^{2}$/${\ensuremath{\sigma}}_{c}^{2}$ and \ensuremath{\varphi}=(1/3 within the one-loop approximation. At zero temperature \ensuremath{\xi} diverges for with ${\ensuremath{\nu}}_{x}$=1/D. Precisely at X=1 the critical behavior of the system is characterized by new exponents; the dynamical critical exponent z is given by z=2+\ensuremath{\varphi}/${\ensuremath{\nu}}_{x}$. For D(1-\ensuremath{\varphi})>2 a new phase appears in the T-X phase diagram, and it is argued that this phase is characterized by spin-glass order.

DOI
10.1103/physrevb.40.4846

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