Abstract
Critical phenomena of continuous phase transitions is one of the most
sophisticated topics in the field of statistical mechanics. Critical
divergences of thermodynamic quantities at a transition temperature $T_c$
are conventionally expressed as a power law in terms of a scaling
variable $T-T_c$. It has been emphasized that the critical power-law
expression is valid only in the immediate vicinity of $T_c$, which is a
very restrictive condition both for numerical simulations and
experiments. In particular, it is difficult to analyze finite size
numerical data of spin-glass models while complying strictly with this
condition. In fact, a naive finite-size-scaling analysis in early
studies of three-dimensional Ising spin glasses lead to inconsistent
estimates for the critical exponent $\nu$ obtained from different
observables.
Recently, we proposed an extended scaling scheme1,2 for critical
phenomena of continuous phase transitions, which is based on the
intrinsic structure of high-temperature series expansions. The extended
scaling expressions are systematically derived for thermodynamic
observables in ferromagnets and in spin glasses. These provide good
leading-order critical representations for a wide range of
temperature, which is significantly enlarged as compared with the
conventional scaling scheme.
With appropriate choices of scaling variables and non-critical prefactors,
in both ferromagnets and spin glasses the leading critical term provides
a good approximation to the true behavior of susceptibility and correlation
length from $T_c$ up to infinite temperature.
The expressions should be of practical importance for estimating
critical exponents in spin glasses, when the
data available from numerical simulations as well as experiments are typically
at temperatures higher than $T_c$ by more than ten percent.
Using the extended scaling scheme, we obtain a consistent set of
critical exponents of the three-dimensional Ising spin glass with
bimodal distribution from finite-size scalings for different
observables, in contrast to previous studies by the conventional
scaling. We also report an application of our scheme to treat the
correction terms for some canonical ferromagnets.
1) I.A.Camplbell, K. Hukushima and H.Takayama, Phys.Rev.Lett. 97,
117202(2006)\\
2) I.A.Camplbell, K. Hukushima and H.Takayama, cond-mat/0612665.
Users
Please
log in to take part in the discussion (add own reviews or comments).