75 research outputs found
The McCoy-Wu Model in the Mean-field Approximation
We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu
model) and study its critical properties in the frame of mean-field theory. In
the low-temperature phase there is an average spontaneous magnetization in the
system, which vanishes as a power law at the critical point with the critical
exponents and in the bulk and at the
surface of the system, respectively. The singularity of the specific heat is
characterized by an exponent . The samples reduced
critical temperature has a power law distribution and we show that the difference between the values of the
critical exponents in the pure and in the random system is just . Above the critical temperature the thermodynamic quantities behave
analytically, thus the system does not exhibit Griffiths singularities.Comment: LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J.
Phys.
The Random-bond Potts model in the large-q limit
We study the critical behavior of the q-state Potts model with random
ferromagnetic couplings. Working with the cluster representation the partition
sum of the model in the large-q limit is dominated by a single graph, the
fractal properties of which are related to the critical singularities of the
random Potts model. The optimization problem of finding the dominant graph, is
studied on the square lattice by simulated annealing and by a combinatorial
algorithm. Critical exponents of the magnetization and the correlation length
are estimated and conformal predictions are compared with numerical results.Comment: 7 pages, 6 figure
Surface critical behavior of random systems at the ordinary transition
We calculate the surface critical exponents of the ordinary transition
occuring in semi-infinite, quenched dilute Ising-like systems. This is done by
applying the field theoretic approach directly in d=3 dimensions up to the
two-loop approximation, as well as in dimensions. At
we extend, up to the next-to-leading order, the previous
first-order results of the expansion by Ohno and Okabe
[Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface
exponents are computed using Pade approximants extrapolating the perturbation
theory expansions. The obtained results indicate that the critical behavior of
semi-infinite systems with quenched bulk disorder is characterized by the new
set of surface critical exponents.Comment: 11 pages, 11 figure
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