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• W3100481691 endingPage "095002" @default.
• W3100481691 startingPage "095002" @default.
• W3100481691 abstract "For the quantum Ising model with ferromagnetic random couplings $J_{i,j}>0$ and random transverse fields $h_i>0$ at zero temperature in finite dimensions $d>1$, we consider the lowest-order contributions in perturbation theory in $(J_{i,j}/h_i)$ to obtain some information on the statistics of various observables in the disordered phase. We find that the two-point correlation scales as : $ln C(r) sim - frac{r}{xi_{typ}} +r^{omega} u$, where $xi_{typ} $ is the typical correlation length, $u$ is a random variable, and $omega$ coincides with the droplet exponent $omega_{DP}(D=d-1)$ of the Directed Polymer with $D=(d-1)$ transverse directions. Our main conclusions are (i) whenever $omega>0$, the quantum model is governed by an Infinite-Disorder fixed point : there are two distinct correlation length exponents related by $nu_{typ}=(1-omega)nu_{av}$ ; the distribution of the local susceptibility $chi_{loc}$ presents the power-law tail $P(chi_{loc}) sim 1/chi_{loc}^{1+mu}$ where $mu$ vanishes as $xi_{av}^{-omega} $, so that the averaged local susceptibility diverges in a finite neighborhood $0<mu<1$ before criticality (Griffiths phase) ; the dynamical exponent $z$ diverges near criticality as $z=d/mu sim xi_{av}^{omega}$ (ii) in dimensions $d leq 3$, any infinitesimal disorder flows towards this Infinite-Disorder fixed point with $omega(d)>0$ (for instance $omega(d=2)=1/3$ and $omega(d=3) sim 0.24$) (iii) in finite dimensions $d > 3$, a finite disorder strength is necessary to flow towards the Infinite-Disorder fixed point with $omega(d)>0$ (for instance $omega(d=4) simeq 0.19$), whereas a Finite-Disorder fixed point remains possible for a small enough disorder strength. For the Cayley tree of effective dimension $d=infty$ where $omega=0$, we discuss the similarities and differences with the case of finite dimensions." @default.
• W3100481691 created "2020-11-23" @default.
• W3100481691 creator A5060853119 @default.
• W3100481691 creator A5090565816 @default.
• W3100481691 date "2012-02-16" @default.
• W3100481691 modified "2023-09-25" @default.
• W3100481691 title "Random transverse field Ising model in dimensiond> 1: scaling analysis in the disordered phase from the directed polymer model" @default.
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• W3100481691 doi "https://doi.org/10.1088/1751-8113/45/9/095002" @default.
• W3100481691 hasPublicationYear "2012" @default.

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