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arXiv:cond-mat/9602043 · Physical Review Letters

Comment on “Renormalized Coupling Constant for the Three-Dimensional Ising Model”

Jae-Kwon Kim

Published Mar 25, 1996• 4 citations
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Abstract

A comment on a recent Letter by Baker and Kawashima (Phys. Rev. Lett. {\bf 75}, 994 (1995)).
DOI
10.1103/physrevlett.76.2402

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In a recent letter, Fytas et al. [Phys. Rev. Lett. 122, 240603 (2019)] study the critical point of the equilibrium random-field Ising model (RFIM) in D=5D=5D=5 by means of state-of-art zero-temperature lattice simulations. We show that their numerical results concerning the virtual absence of violation of supersymmetry and the characterization of the main corrections to scaling are in full agreement with our predictions by means of a nonperturbative functional renormalization group and with the existence of a critical dimension DDR≈5.1D_{DR}\approx 5.1DDR​≈5.1 above which supersymmetry and dimensional reduction are valid at the fixed point and below which they break down.
In a recent letter -Phys. Rev. Lett. 73, 3331 (1995)-, the conclusion was reached that, in the one-dimensional Calogero model, only the second virial coefficient is affected by the statistical parameter ααα, where ααα is related to the coupling constant κ/xij2κ/ x_{ij}^2κ/xij2​ of the Calogero interaction by κ=α(α+1)κ=α(α+1)κ=α(α+1). We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.