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arXiv:cond-mat/0005176 · Physical Review Letters

Comment on “Critical Behavior of the Randomly Spin Diluted 2D Ising Model: A Grand Ensemble Approach”

Aernout C. D. van Enter, Christof Külske, Christian Maes

Published Jun 26, 2000• 16 citations
arXivHTMLPDF

Abstract

We point out that the "disorder potential" employed in the grand ensemble approach is ill-defined in considerable generality.
DOI
10.1103/physrevlett.84.6134

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Kühn and Mazzeo Reply:

Reimer Kühn, Giorgio Mazzeo

We reply to a comment of Van Enter, Kuelske and Maes (cond-mat/0005176) on our letter "Critical Behavior of the Randomly Spin-Diluted 2-d Ising Model - A Grand Ensemble Approach", Phys. Rev. Lett. {\bf 73}, 2268-2271 (1994).

arXiv:cond-mat/0005177•Physical Review Letters•Jun 26, 2000•5 citations

Comment on "Exact Critical Behavior of a Random-Bond Two-Dimensional Ising Model."

Andreas W. W. Ludwig

Physical Review Letters•Feb 20, 1989•2 citations

Critical phenomena in 2D anisotropic spin systems with weak disorder

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The critical behavior of 2D anisotropic systems with weak quenched disorder described by the so{called generalized Ashkin{Teller model (GATM), including the Ising model with random bonds, the dilute Baxter model, the impure N{color Ashkin{Teller model, and minimal conformal eld theory models (MCFTM) with c < 1 (c is the central charge) perturbed by randomness is discussed.All these models except MCFTM were found to belong to the Ising model universality class.Critical exponents of disordered MCFTM are calculated within perturbative expansions in the powers of = c 1=2. RG ows exhibit the rounding of uctuation{driven rst{order phase transitions by disorder.

Journal of Physical Studies•Jan 1, 1998•1 citation
The critical behavior of the 2D spin diluted Ising model is investigated by a new method that combines a grand ensemble approach to disordered systems with phenomenological renormalization. We observe a continuous variation of critical exponents with the density $\ensuremath{\rho}$ of magnetic impurities, respecting, however, weak universality in the sense that $\ensuremath{\eta}$ and $\frac{\ensuremath{\gamma}}{\ensuremath{\nu}}$ do not depend on $\ensuremath{\rho}$ while $\ensuremath{\gamma}$ and $\ensuremath{\nu}$ separately do. Our results are in complete agreement with a recent Monte Carlo study.
The critical behavior of 2D anisotropic systems with weak quenched disorder described by the so{called generalized Ashkin{Teller model (GATM), including the Ising model with random bonds, the dilute Baxter model, the impure N{color Ashkin{Teller model, and minimal conformal eld theory models (MCFTM) with c < 1 (c is the central charge) perturbed by randomness is discussed.All these models except MCFTM were found to belong to the Ising model universality class.Critical exponents of disordered MCFTM are calculated within perturbative expansions in the powers of = c 1=2. RG ows exhibit the rounding of uctuation{driven rst{order phase transitions by disorder.