Domain scaling and marginality breaking in the random field Ising model

Details Domain scaling and marginality breaking in the random field Ising model Domain scaling and marginality breaking in the random field Ising model

1995-05-12

arxiv.org/abs/cond-mat/9505055v1

Physics

Condensed Matter

ReVTeX v3.0, 19 pages plus 19 figures uuencoded in a separate file. These are self-unpacking via a shell script

Scientific paper

10.1088/0305-4470/29/23/011

A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A h^{-\gamma}\right)$ in $d=2$, and for $d=2+\epsilon$ power law behaviour with $\nu = 2/\epsilon \gamma$, $h^\star \sim \epsilon^{1/\gamma}$. Here, $\gamma = 2,4/3$ (lattice, continuum) is one of four rough wall exponents provided by the theory. The analysis is substantiated by three different numerical techniques (transfer matrix, Monte Carlo, ground state algorithm). These provide for strips up to width $L=11$ basic ingredients of the theory, namely free energy, domain size, and roughening data and exponents.

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