Аннотация
A powerful computational method for dealing with correlation functions in
magnetic systems, based on damage-spreading simulations, is reviewed and
tested for two-dimensional ferromagnets.
Exact relations involving special kinds of damage
and correlation functions, as well as the corresponding order parameters,
are used.
The efficiency of the method arises through a significant reduction of the
finite-size effects,
with respect to conventional Monte Carlo simulations. Correlation
functions, which represent usually a hard task within this later procedure,
appear to be much easily estimated through the present damage-spreading
simulations. The method is applied to two well-known ferromagnetic models
characterized by nearest-neighbor interactions on a square lattice, namely,
the $q$-state Potts and Ashkin-Teller models.
In the first model, the effectiveness of the technique
is illustrated by an accurate estimate of the exponent $\eta$, of the
spin-spin correlation function, for $q=2,3,$ and 4, with rather small
lattice sizes, whereas in the cases $q 5$, an analysis of the
magnetization is consistent with the well-known first-order phase transition.
For the Ashkin-Teller model, we concentrate our analysis along the
Baxter line, well known for its continuously varying critical exponents;
eight different points along this line are investigated.
The efficiency of the method is confirmed through precise estimates of the
critical exponents associated with the order parameters (magnetization and
polarization), as well as with their corresponding correlation functions,
along the Baxter line of the Ashkin-Teller model, in spite of the small
lattice sizes considered.
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