Phase diagrams
and
universality classes of random antiferromagnetic spin ladders
J.
A. Hoyos and E.
Miranda
Phys.
Rev. B 69, 214411 (2004); arXiv:cond-mat/0404444.
Disclaim
This is my first paper and has an interesting history.
Eduardo, then my PhD advisor, was interested in applying the Ma, Dasgupta and Hu
RG to the Giamarchi
and Schultz problem. We then decided to learn the SDRG and check my
program on the spin ladders, just to warm up. (I don't remember why the
ladders since it is more difficult than the chains.)
It happened that my dynamical exponent for the two-leg ladder was not
in agreement with those obtained by Rieger and Iglo's
group. Fortunately, Yusuf and Yang
had done the same calculation for the magnetic susceptibility, and I
was obtaining the same thing. So I thought that Rieger and Igloi's
group had
probably just mixed the values of some parameters. Furthermore, the
conclusion they wrote was precisely correct.
So far so good. Then, I decided to do the same check for the zigzag
ladder, and my findings were
completely different from Rieger and Igloi's group. Unfortunately,
there was no
other paper on the zigzag ladder to compare with. It was 2002/2003 at
the
time.
After starting to understand what is a Griffiths phase
and a Large Spin
phase in the context of these spin systems, I realized that
frustration have an important role in the zigzag ladder. I saw that the
spin moments were increasing when the energy scale was lowered and that
the FM couplings were as strong as the AF ones. This is what is seen in
the large spin phase. I then checked that the mean distance between the
spin clusters and the mean square of magnetic moment scale in the same
manner, exactly as in Large Spin phase. I showed that to Eduardo and he
became very excited with this. Short later, I then asked myself if the
ladder, somehow, mimic the chain. It was clear that long-ranged
couplings appeared after renormalizations but I always had the feeling
that long-range interactions would screw up this physics. After
discarding couplings below a very low cutoff, I saw that the
long-ranged couplings vanish near the fixed point. Naturally, I came
back to the two-leg ladder in order to see in which chain that ladder
renormalize into. It was clear that it would be the dimerized ladder,
as confirmed numerically.
After having those conclusions, Eduardo told me to start writing a
paper. (Had no idea in how doing that at the time.) Unfortunately, one
or two weeks later, I saw in cond-mat a preprint from Yusuf and Yang
bringing nearly the same conclusions for the zigzag ladder. At the
time, my
English vocabulary was poor and Eduardo (better say Yusuf and Yang)
taught me one more phrasal verb: scoop up!
It then took me an eternity to write the paper and another one from
Eduardo to rewrite it.
Eduardo decided to not submit it to arXiv before it was published
(don't ask me why). Fortunately, the 2 referees liked the paper. (Maybe
because we showed in a very clean way that the ladders renormalized
into chains.) I
remembered that one of them asked to put error bars on the data.
Eduardo asked me
to do so and I got somewhat pissed off. I think that it is because I
have some unconcious problem in remembering where I put the data.
Durham, June 12th, 2008